The joke about AEG Telefunken goes like this:

Three men approached a conference table, each representing one of Europe's giant electrical firms. Each found on his seat a thumbtack standing straight up. The man from Phillips of the Netherlands swept his away with a forceful stroke. The man from BBC of Switzerland picked his up and said perhaps he could find a use for it. But the man form AEG Telefunken of West Germany sat directly on the tack, declaring somewhat painfully that his boss must have had something in mind when he left it there in the first place.

The point is not lost of the folks at AEG. Months of losses, cutbacks, selloffs and reorganizations have made the company a sorry target for grim boardroom humor. In the executive suites of Germany's largest banks and corporations, though, they are not laughing about AEG. They are trying to save it.

This century-old firm, literally a household name in West Germany for electrical appliances and home entertainment equipment, is an embarrassment to the efficient, prideful ranks of Germany industry.

The country's ninth largest concern with $7.9 billion in sales last year, it suffered sizable losses in three of the last six years. So far accumulated losses have reached $700 million, virtually exhausting the company's capital and reserves. Dividend payments ceased in 1973, and since 1975 the company has let go 14,200 workers, or 11 percent of its work force, in a country in which layoffs just are not supposed to happen.

With the nation approaching a general election this autumn, and further job cuts probable at AEG, the company was threatening to become a problem child for the government. It appeared as though West Germany would have a Chrysler on its hands.

The notion of a government bail-out was hardly agreeable to the country's banks and businesses -- or to the government, for that matter. So the private sector stepped in with a rescue plan of its own, which shareholders approved at an extraordinary meeting here on Jan. 15 -- an extraordinarily long, noisy and turbulent meeting. And on Jan. 20, a new company chief was named.

The rescue, or attempted rescue, has been hailed as a sign that West Germany's free enterprise system can take care of itself. "As the AEG case should show, the free enterprise system is strong enough to handle such a crisis," spoke the leading Frankfurter Allgemeine newspaper in a recent editorial.

But the banks spearheading the rescue effort have more than a capitalist idea at stake. They have loans outstanding of $1.7 billion to AEG. Also at risk is the special relationship in West Germany between the banking and business communities.

Under German law, banks can act as brokerage houses, hold industrial interests and act as banks all at the same time. Such an assortment of activities is not permitted at U.S. banks.

As one might imagine, the so-called universl banking system in West Germany results in the banking sector having considerable economic power -- too much, some say, and the legislature is expected to review banking law this year. German banks own about 40 percent of AEG's outstanding stock.

In their defense, German bankers often claim that by sitting on the boards of the companies they lend to and voting for individual investors as well, they are more effective watchdogs, than, for example, independent U.S. directors.

However, it has been said that part of the problem at AEG was that the banks did not understand the changing diversified nature of the electrical industry in which they had invested.

There were other problems, of course. Every analyst seems to have his favorite. Add them all up -- wrong product mix, poor management, import competition, foreign exchange problems, bad luck -- and they total an overwhelming combination of disaster.

World War II and the subsequent division of Germany took its toll on the firm. More than 80 percent of its assets ended up belonging to East Germany. Afterwards, in a decision that was to haunt the company, AEG chose to build up at home before advancing strongly overseas. This seemed natural enough at the time, particularly because West Germany was proving a buoyant market year after year.

But rival Siemans took another course, expanding early overseas, and this later turned out to be very shrewd.

AEG's performance often is compared unflatteringly with the stunning performance of its bigger competitor in the electrical field.Until recently the two groups were in fact partners in nuclear power station construction, each holding a 50 percent stake in Kraftwerk Union (KWU. But here again, AEG ended up on the short end.

AEG had been the first in the nuclear field in West Germany in the late Sixties. In 1971, it formed KWU with Siemens. In joining, each company agreed to be responsible for its own losses for earlier projects. These began to mount for AEG, in part due to faulty designs, in part due to changes in safety standards.

In theory, power station construction would appear to be precisely the kind of field in which AEG could build its future, relying on traditional skills. But, again in contrast with Siemens, it has remained highly dependent on demand for consumer goods where the foreign challenge -- particularly from the Far East -- is strong and growing.

In 1978, one-third of its world sales came from consumer goods. Its other business areas include power engineering and industrial systems (25 percent), telecommunication and transportation systems (18 percent), industrial and electronic components (17 percent) and office machines (6 percent).

When it tries to sell overseas, AEG is handicapped by having most of its plants at home. Roughly 80 percent of its work force of 155,000 is paid in appreciating marks, and the high German exchange rate also makes for a more costly product overseas. While domestic sales rose 8 percent last year, foreign sales fell 7 percent.

Not that this electrical giant has been sitting helpless. After suffering substantial losses in 1974, the company hired a new chief executive: Walter Cipa, fresh from reorganizing a West German oil company. He restructured management and reorganized divisions, severing unprofitable lines, maintaining spending on research and development, and concentrating on such expanding divisions as data processing. To this end, AEG recently bought 25 percent of the U.S. firm Modular Computer System Inc.

But Cipa's tough approach and abrasive personality caused a number of people to leave and company morale to sink. His exit was part of the price of the new recovery plan.

His replacement will be Heinz Durr, 46, an independent businessman from Stuttgart who had been running a medium-sized corporation that makes car paint machines.

Durr is typical of the young, entrepreneurial business breed, but whether he will be able to manage the bureaucratic and troubled ranks at AEG is a question industry analysts have posed.

In any case, Durr himself announced he was taking the job for the sake of "a challenge." He was the handpicked candidate of Hans Friderichs, the chief executive of Dresdner Bank, who himself last month became the chairman of AEG's supervisory board.

As a former finance minister, Friderichs is a well-known and respected figure in West Germany, and his presence now at AEG signals the more influential role the the banks intend to play in the recovery of the company.

Under the terms of the rescue plan, a consortium of 25 banks led by raise $530 million for AEG. The banks also have agreed to restructure $1 billion of long-term debt into an eight-year loan with a three-year grace period.

In addition, insurance companies and leading corporations have said they will subscribe to a so-called "solidarity loan" of about $80 million in unsecured promissory notes with option rights to purchase company shares. A further solidarity loan also is being considered.

Shareholders approved the plan last month, but hardly enthusiastically. They have been asked to sacrifice, too. The worth of their holdings will shrink because they are to receive one new Telefunken share for every three old ones, with both old and new having the same par value.

The shareholder meeting lasted from morning to midnight and was filled with criticism of the management and calls to punish those responsible for the sorry state of the company. One shareholder took nearly 3 hours to ask more than 60 questions and refused to be silenced. "We have a right to answers," he said. "We are not under pressure from Russian tanks."

Outside, employes demonstrated against a proposed cut of 13,000 more jobs this year. In recent months, 1,000 workers staged a march on Essen city hall where an AEG turbine plant closed, and another 3,000 protested a closing in Hannover.

Resolving labor problems will be among Durr's first tasks. But with fresh cash now coming in, the company's primary aim will be to develop products that sell.