For two decades, ITT Corp. symbolized for many people the acquisitive conglomerate: Under its former chairman, Harold Geneen, it took over some 350 companies and its operations extended into more than 80 countries.

Today, ITT has acquisition on its mind again, only this time there is speculation that the telecommunications and insurance conglomerate may itself be the target.

The speculation on Wall Street began last summer, just after the company made the surprise announcement that it would cut its annual dividend by nearly two-thirds, from $2.76 to $1 a share. The announcement, which came after ITT predicted that its profits would drop from last year's $675 million to about $435 million this year, immediately sent ITT's stock spinning downward from $30 to $21 a share, nearly half the company's book value.

Speculation intensified again last week when it was disclosed that Minneapolis financier Irwin L. Jacobs had purchased about 3 million ITT shares, or about 2 percent of the company's outstanding stock. Some financial analysts predict that Jacobs is seeking to break up the conglomerate and sell all or parts of it piecemeal.

The price of the company's stock is now back around $30. But even at this level, analysts note that the liquidation value may be as high as $55 to $60 a share.

"The only reason to raid ITT is to get control and liquidate it," says Robert Sullivan of Paine Webber Mitchell Hutchins. "You could sell the pieces and come out ahead of the game."

Herbert E. Goodfriend, an analyst with Prudential Bache Securities, adds: "While Jacobs hasn't made any formal steps, the presumption is that he will pressure management to consider asset liquidity of the companies that are not as productive as they should be."

Having been the acquirer for so many years, ITT is fortifying its guard to make sure it does not become the acquired this time around.

Rand V. Araskog, ITT's chairman, president and chief executive, has put out a warning about anyone interested in trying to take his company over: "They're in for the fight of their lives."

ITT already has hired a public relations firm that specializes in proxy fights and takeovers, as well as the law firm of Cravath, Swain & Moore. "We'd be foolish not to take the takeover speculation seriously," said ITT spokesman James P. Gallagher. "Whether it is possible or not, we have got to be prepared."

ITT also has hired two investment houses to provide advice on how to maximize the company's assets. Among the options being studied is the possible sale of several of ITT's major subsidiaries.

Yesterday, with the price of ITT's stock down $1.25 to $30.75, some financial analysts began to discount rumors that Jacobs was out to take over the entire company.

Brian R. Fernandez of Nomura Securities International Inc. noted that he was skeptical because Jacobs has not kept his transaction secret -- usually a top priority for anyone trying to make a move for a company.

Instead, Jacobs notified Wall Street that he had bought about 3 million shares last week when an unusual trading mix-up on the floor of the New York Stock Exchange made it appear that he had bought less than he intended.

"This has been one of the least secret stock accumulations I've seen in a long time," Fernandez said.

Other analysts noted that any takeover of ITT would be too expensive for any one party. With nearly 140 million shares outstanding, ITT could cost more than $5 billion to acquire.

"There is nobody around with enough money to do it," said Larry Baker of the E. F. Hutton Group Inc.

Nonetheless, analysts noted that with Jacobs and other investors -- including the Pritzker family of Chicago and Denver oilman Philip F. Anschutz -- reportedly buying large chunks of ITT stock, it is very likely that there will be some outside pressure on the company to make major changes in its operations. If not, predicted one analyst who declined to be named, there could be a fight for control of the company.

Jacobs recently succeeded in forcing an ownership and management restructuring of Walt Disney Productions after he bought 7.7 percent of the company's stock.

"It is time for action at ITT -- whether it comes from within or without," said Harry Edelson, managing partner of Edelson Technology Partners. "I think they will have to do major surgery in the next few months."

Although ITT hired the two investment bankers last July to consider such surgery, they may have to move faster than they had earlier anticipated given Jacobs' interests, analysts predict.

Analysts said likely targets for divestiture include ITT's Sheraton Hotel chain, its automotive-parts manufacturing and service companies, Eason Oil and the timber subsidiary, ITT Rayonier Inc.

Likely to remain within the company are its telecommunications and financial services operations, including the Hartford Fire Insurance Co.

The spin-offs will not be the first for ITT. Last summer, the company sold ITT Continental Baking Co., the maker of Wonder Bread and Twinkies, to Ralston Purina Co. for $475 million. It was one of 60-some divestitures since Araskog took over the company five years ago. ITT's assets at the end of 1983 totaled $986 million -- less than half what they were when Geneen left as chairman in 1979.

The sale of its properties would go a long way toward helping ITT's balance sheet, which is seeing declining earnings, partly because of the increased competition in the telecommunications industry and partly because its insurance subsdiary, like other insurance companies, has failed to turn around from a four-year slump. In fact, as a result of an increase in weather-related losses last year, the company's profits dropped more than expected, forcing the subsidiary to lay off many workers.

ITT also has trimmed its corporate staff, as well as 800 employes in some of its domestic telecommunications manufacturing plants.

One financial analyst who declined to be named noted that ITT's financial performance was affected by more than just competition and the troubled insurance subsidiary. "It's a very poorly run company. . . . It's a centralized bureaucracy where everyone is writing reports and filling out five different forms and no one is worrying about making money. The paper pushers make it to the top, not the people who know how to run a business."

Geneen, commenting in a recent interview on the change in the company's style since his tenure there, noted that "when I look out at the ITT building after 6 p.m., most of the office lights are out. It's a different company now."