Prince George's County Executive Lawrence Hogan, a Republican, claimed a victory yesterday.

The all-Democratic County Council said it was not much of a victory and accused Hogan of engaging in "political chicanery" and general "sneakiness."

So went another engagement between the executive and the council in their continuing war over appointments.

At issue in the latest clash was Hogan's appointees to the Prince George's Planning Board, the county's half of the suburban Maryland-National Capital Park and Planning Commission.

Hogan's first appointee, University of Maryland Prof. John Cumberland, was vetoed by the council in April after council members accused Cumberland of harboring an anti-development philosophy.

Hogan's second nominee was William Goodham, a former Democratic state senator who long has been at odds with the Democratic party regulars and therefore could anticipate rough going with the council's Democratic incumbents. Goodman was heavily backed by the party's so-called independents, who defeated some candidates on the party's slate in 1978.

Yesterday, the council vetoed Goodman as well, accusing Hogan of submitting his name simply to aggravate tensions among Democrats.

Then the subtleties and surprise began to pile up.

Hogan noted that the council had failed to take up Goodman's appointment within the 30 days prescribed by state law. The council thought it had 30 business days to act, but was told by legal experts that it was wrong.

Therefore, Hogan maintained, Goodman's appointment had automatically gone into effect.

Not so, countered the council. On rechecking, the council found it also had allowed more than 30 days to pass before it vetoed Cumberland's appointment in May.

Since both Cumberland and Goodman had been intended as the replacement for one man -- former planning commissioner W. C. Dutton -- Cumberland, rather than Goodman, would take the job, the council declared.

Hogan, buttressed by legal research by the county attorney, countered that, in fact, both Cumberland and Goodman, are now planning commissioners.

This is because on June 15, during the heat of the dispute, the term of Commissioner John Churchill expired. That meant there were two vacancies and room on the commission for two new members, Hogan said.

The dispute now revovlves around this last point. The council says Goodman cannot sit on the commission because Hogan specifically nominated him for Dutton's seat and, beside, only one vacancy existed at the time the appointment was made.

The council voted to have the county attorney, who council members criticized earlier for failure to warn of the calendar problem, file suit if necessary to prevent Goodman from being sworn in.

"It's dizzying, just dizzying," exclaimed Council member Ann Lombardi. "It's just dastardly, this marionetting. This guy [Hogan] is just sitting up there pulling whatever strings he can find."

Hogan spokesman Stephanie Bolic responded: "He's not pulling strings, he's turning pages in a law book. This was not sneakiness, it's smarts."

Both the council and Hogan as well as Goodman's supporters have asked the state attorney general to decide whether a second commission vacancy existed at the time Goodman was being considered and, if so, whether he should be allowed to fill it.