All is quiet at Computer Network Corp.'s sleek white headquarters on MacArthur Boulevard NW--deceptively quiet. Employes speak softly while the company's scores of computers silently work.

But the quietude belies the fact that the company's management is engaged in a fierce and increasingly vociferous battle with several of its stockholders.

In the courts and before the Securities and Exchange Commission, a handful of shareholders who together own nearly a quarter of the company's stock are accusing Comnet's officers of mismanaging the company and using its assets for their own benefit, to entrench themselves in office at the stockholders' expense.

Management, on the other hand, is charging the dissident shareholders with trying to take over the company at an unjustifiably low price and with trying to grab Comnet's large chunk of cash and stock in two promising computer-equipment companies. Management contends that it must protect all of the company's 1,400 stockholders from such a move--even if it is being made by company stockholders.

The antagonism between the two sides grows more bitter by the day, as each side steps up its fight before the courts and the SEC, in anticipation of a showdown at the company's annual meeting later this summer.

The fight has brought a lot of attention to the relatively small company that specializes in computer time-sharing and management.

For the fiscal year that ended in March 1982 (the latest annual figures available), the company had $12.8 million in revenue--down from $19.3 million in fiscal 1981 and $21.2 million in fiscal year 1980. Its profits totaled only $500,000 in fiscal year 1982. That money came not from its computer operations but rather from interest the company had collected on its large amount of cash reserves.

Comnet's chairman, president and chief executive officer, Lee Johnson, said the company's earnings have improved somewhat since that time, but he declined to reveal exact figures until Comnet's annual report is released later this month.

The disgruntled group of stockholders, led by New York stockbroker John Spohler, is very displeased about the company's failure to earn a profit on its chief business operations.

But the dissidents save their strongest criticism for a series of recent actions taken by Comnet's management designed to prevent a takeover by any unfriendly company or group of investors.

At issue are:

* A special compensation plan in which Comnet must pay five years of salary and benefits to the company's top four officers if any company or group of individuals tries to take over the company. Initially, when Comnet officers adopted this plan last year, they guaranteed 10 years of salary and benefits to the top officers. But last month, after dissident shareholders loudly complained that this plan could turn over as much as 50 percent of the company's assets in a takeover, the compensation plan was cut back.

* A new stock option scheme that would automatically accelerate, upon announcement of a tender offer or proxy fight, the vesting and redemption of stock options granted earlier to the top officers.

* A change in the way the company has elected its board of directors so that, instead of permitting stockholders to vote on the entire board of directors each year, stockholders would be permitted to vote on only two director slots each year. This change makes it impossible for stockholders to change the company's management and direction in a single year.

* The acquisition of Data Systems Consulting Corp., a New York company that provides computer and data proccessing services to nursing homes, for $800,000 and 227,000 shares of Comnet stock, or about 12 percent of the company's outstanding shares. The stock has been placed in a voting trust managed by Comnet's directors, who before the establishment of the voting trust owned and had control of less than 6 percent of Comnet stock.

Taken together, Spohler says these measures are designed to "entrench the current management in office."

The changes "were effected solely or principally for the purpose of perpetuating [Comnet's officers] in office, contrary to the principles of corporate democracy, to limit the ability of dissident stockholders to wage a proxy fight, and to thwart the acquisition of Comnet by third persons," Spohler charges in a lawsuit filed in U.S. District Court here.

"The management has acted in its own selfish interest to the detriment of Comnet stockholders," Spohler added in an interview. Spohler said this was "particularly galling" considering that Comnet management owns such a small share of the stock.

As much as he and his fellow disgruntled shareholders would like to fight these actions, Spohler complained that they are deterred from trying to get other shareholders to overturn the measures because any such move could be construed as a proxy contest, which in turn would trigger the compensation and stock-option scheme.

If that happened, Spohler said the assets of the company would be sharply eroded and the value of his stock would decline.

Consequently, Spohler and his colleagues are trying to overturn these actions in other arenas. In the U.S. District Court, Spohler is asking that they be declared "null and void."

At the same time, he has sought a court order barring Comnet from acquiring another company in the near future. Spohler fears that Comnet may attempt to buy a company through the issuance of stock, which in turn would be placed in another voting trust. This would not only dilute the shares but place more stock in the hands of the management, which would then have more power to turn down a stockholder challenge. However, a federal appeals court rebuffed Spohler's bid last week, saying it was inappropriate to bar any merger until one was announced.

Meanwhile, Spohler is trying to win SEC approval for a series of shareholder proposals that would overturn the recent measures. If successful, the stockholders would be able to vote on these proposals during the annual meeting later this summer.

Comnet's management, however, charges that the shareholder proposals are improper because, among other things, they are designed to circumvent the court, in the event that it rules against them.

"Be assured, we are not motivated by ambition, ego, or solely personal considerations, but rather wish to insure the appropriate, productive use of corporate assets to maximize shareholder values," Spohler said in explaining why he is spending an increasing amount of his time fighting Comnet's management, especially Johnson.

However, as Johnson sees it, the motives of Spohler and his colleagues are far from charitable.

As Johnson explained in an interview last week, "the group"--as he calls the dissident stockholders--was trying to take over a cash-rich company and strip it of its cash and stock in two promising new computer companies for a price far below the company's real value.

The board adopted the antitakeover measures in the fall of 1981, when there was a rash of takeovers of firms with large cash reserves. At the time, Johnson said, Comnet had approximately $13 million in total assets, of which over $7 million was in cash and highly liquid assets. The company's stock was trading for about $4.25 a share, even though an analyst calculated that the value of the stock, based only on the company's cash position, was $4.50.

"Is it possible that they had designs on the company?" Johnson asked. "But instead of coming to the company and discussing an offer, they thought they could acquire control, spin off [the two new computer companies] and buy it for less cash than was on the books. Is it possible that that was a motive?"

Suspecting as much, Johnson had Comnet file suit against Spohler for failing to file the proper forms before the SEC to let the public know his true intent. Johnson has since dropped the suit, saying Spohler has now submitted the proper forms.

Even so, Spohler says that he has no intentions of taking over Comnet. "The furthest thing from my mind is running a company in D.C.," he said. "I'm quite successful in my own right. I don't need this."

Nonetheless, Spohler and his fellow stockholders say they may be forced into a showdown later this summer if they can't win their case before the SEC or the courts.