International Business Machines, the giant computer company, yesterday announced a 56-cent increase in its quarterly dividend.

Its board of directors also recommended that shareholders approve a 4-for-1 stock split at the company's annual meeting next April 30.

News of the payout increase and the proposed stock split sent IBM prices soaring and helped boost the Dow Jones average of 30 industrial stocks 2.34 points. The Dow Jones index fell sharply on Monday after the oil-producing countries announced a bigger-than-expected increase in petroleum prices.

*Trading in IBM was halted briefly while the announcement was made-shortly after the opening 10 a.m. bell-but the stock climbed sharply when trading was resumed, closing at 2817/8 up 113/4 over its Monday close.

IBM is the second most expensive stock traded on the New York exchange, after Superior Oil, which closed Tuesday at 3221/2. An IBM spokesman said the board felt that the stock split would bring the price of IBM shares down to a level "attractive to small investors."

An IBM spokesman said that there were 145,778,258, shares of IBM stock outstanding at the end of September. After the split, there will be about 580 million shares outstanding.

Wall Street had anticipated an IBM stock split for more than a year, but analysts said the size of the split was much bigger than anticipated. The last time IBM stock split was in 1973, when investors received five shares of stock for each four they owned.

If stockholders approve the board of directors proposal, soon after May 10, 1979, they will receive three more shares of IBM stock for each share they already own.

At the end of 1973, IBM's dividend rate was $4.48 a year. With the 56-cent a quarter increase announced yesterday, IBM has earned $2.096 billion on sales of $14.638 billion. For the first nine months of 1977, IBM's earnings were $1.922 billion on sales of $13.095 billion.

Analysts saif the dividend increase suggests that IBM is in a strong cash position and does not anticipate heavy increases in capital outlays in the coming years.

IBM has long been the nation's dominant computer company, although hundreds of firms have moved into the field. The company now is gearing up to invade a field long-dominated by American Telephone and Telegraph.

The computer giant wants to wangle a big share of future long-distance communications of computer data. AT&T has fought a losing battle before the Federal Communications Commission over the last 10 years to hold on to its near-monopoly of telecommunications equipment and services.

An IBM challenge to AT&T in data communication promises to be a big-stakes regulatory struggle.

In fact, Donald Brown, vice president for research at Dean Witter Reynolds, suggested, the IBM stock split may represent a move by IBM's board to increase sharply the number of shareholders and give the computer giant--the nation's political base in any regualtory square-off with AT&T.