Lawrence J. Hogan, a former Republican congressman from Maryland, resigned yesterday as esecutive director of Associated Builders and Contractors after losing an internal power struggle that involved some political intrigue as well as a dispute over management techniques.

Hogan had actually been fired from the post last week by teh national association's president, Joseph A. Burton, who said that he and Hogan had not seen "eye to eye." The dismissal had been challenged by Hogan, who argued that only the ABC board of directors had the power to take such action.

The 150-member board met in emergency session here yesterday morning to consider whether Hogan should be dismissed only to discover that a resignation agreement between Hogan, Burton and their two lawyers had been worked out the night before. The agreement was that Hogan would resign graciously and that neither man would say anything disparaging about the other.

Thus in press releases that had been prepared before the board of directors formally accepted the resignation, Burton was quoted as calling Hogan "a man of competence, dedication and ability," and Hogan responded by calling Burton "a fine man dedicated to A.B.C."

The press releases gave no explanation for the firing, nor, according to several sources, did Burton or other association leaders explain Hogan's earlier dismissal at yesterday's closed-door board of directors session at the Hyatt Regency Hotel. "They left us in the dark," said one member of the board. "They said they would set up a committee to report back to us on it."

Another board member said he believed the firing resulted from personal and political differences."Joe and Larry have been fighting for the last 14 months, since Larry came on board," he said. "Burton's a Democrat and Hogan's a Republican. They're both from Maryland. The're both strong-willed. It was a strained situation from the start."

Although Burton never publicly outlined his differences with Hogan, the allegations were so widespread at the ABC convention headquarters at the hotel yesterday that Hogan saw fit to respond to them with what he called a "truth sheet." The allegations, as Hogan saw them, were that he had replaced the old ABC staff with unexperienced political cronies.

Hogan conceded that he had fired three people and that one of his new employes, Ross Whealton, a former assistant to U.S. Rep. Robert Bauman (R-Md.), had political connections.He argued that Whealton was an outstanding political strategist who would get the association's political action program off the ground.

Hogan said that of the other eight people he hired, only one, former Maine Gov. John Reed, could be called a politician. "And," said Hogan, "I never met Reed until I interviewed him for the job."

"If Mr. Burton's action is upheld, no executive worth his salt will ever work for national ABC. And, without doubt, the effect will be felt on local chapters seeking to attract and keep quality staff."

Hogan did not look or sound like a particularly sad man yesterday. In fact, he looked and sounded like a man who was about to return to his first calling - politics. Only last week, during an interview on GOP politics in his home county, Prince George's, Hogan had said that he would not leave his ABC job to run for office this year.

"I'm reconsidering that right now," he said, a smile moving into shape. "I may run for governor (he did that in 1974, losing in the GOP primary to Louise Gore), I may run for county executive. I may just try to become a rich lawyer."