Eight governors joined President Carter at Camp David last night at the start of what White House officials called a "domestic summit conference" that is likely to last through much of next week.

The govenors were the first of what is expected to be several groups to be summoned to the presidential retreat in Maryland Catoctin Mountains over the next several days. The sessions clearly will be searching reviews by Carter and his aides on the directions of domestic policy and how that policy is made.

White House officials stressed yesterday that topics at the Camp David meetings will include more than the immediate issues of energy and economic policy. They left open the possibility that the meetings will result in shakeups in the White House staff and Cabinets as well as in the president's leadership style.

"What is being talked about is how to give a different direction to the leadership and management of the country without changing presidents," said one Carter associate.

Speculation on Cabinet changes has centered on possibility that Energy Secretary James R. Schlesinger Jr. will be fired or transferred to some other post. Carter has said repeatedly that he has full confidence in Schlesinger.

In many ways, the Camp David meetings were reminiscent of another domestic summit conference, also held at Camp David, that Carter called in April 1978.

With his political fortunes then sliding badly -- although nowhere near their present low point -- the president Cabinet officals for a weekend of talks. As a result, Cabinet authorityy was strenghtened and the White House staff was reorganized slightly and beefed up.

But presidential aides conceded yesterday that many of the problems that plagued the administration last year have continued into 1979 and that some of Carter's advisers have been urging him to act boldly before it is too late to salvage any change of re-election in 1980.

"I thing this is an attempt to look at the root causes, not just the symptoms," said one official. "There is a recognition that some changes may be needed around here. I think there is a recognition that if we are at 25 percent in the polls, there might be some reason for it."

It remained unclear yesterday exactly what triggered the president's decision to call this second summit conference on domestic policy and the internal problems of his administration. He was to have delivered a nationally televised speech on energy Thursday night. But Carter abruptly canceled the speech Wednesday and set in motion what his senior aides described as a review of overall domestic policy-making, not just questions of energy and the economy.

There was widespread agreement yesterday that in canceling the speech and retreating to the seclusion of Camp David, the president both heightened the drama surrounding the meetings and his political stakes in what the sessions produce.

"The circumstances, including the mystery and the delay, means that Carter himself is upping the ante on what comes out of this," one official said

The White House yesterday continued to provide only scant information about the president's activites. Officials said they expected the Camp David meetings to last well into next week.

"The president will not be returning to Washington until he's seen the people he wants to see and has had time to assess what he has heard," one aide said.

The first group that Carter met was the governors. They gathered at the White House late yesterday afternoon and were flown by helicopter to Camp David, where they remained overnight.

The governors were Julian Carroll of Kentucky, chairman of the National Governors Association; Hugh Carey of New York; Ella Grasso of Connecticut; Brendan Bryne of New Jersey; Otis Bowen of Indiana; James Hunt of North Carolina, George Busbee of Georgia and Dixy Lee Ray of Washington.

Bowen, the incoming chairman of the governors association, was the only Republican in the group.

The president invited the governors to Camp David yesterday after canceling his plans to fly to Louisville, Ky., today to attend the governor's annual conference. He was to have addressed the group tommorow. The White House said that the president's wife Rosalyn, and Vice president Mondale would travel to Louisville for the meeting.

Mrs. Carter was among those at Camp David with the president last night. Others present when the governors arrived, and who have been with Carter since Thursday, were White House political adviser Hamilton Jordan, press secretary Jody Powell, media adviser Gerald Rafshoon and pollster Patrick Caddell.

Carter's longtime friend and adviser. Atlanta Lawyer Charles H. Kirbo, arrived at the presidential retreat late yesterday.

White House officials said earlier that Carter planned a series of meetings with persons within and outside the government. Cabinet members are expected to be among those who will attend meetings at Camp David next week. But the White House refused to say exactly which groups and individuals the president intends to see in the next few days.

Among those Carter conferred with yesterday by telephone was Robert S. Strauss, his special envoy to the Middle East peace talks between Israel and Egypt. In Alexandria, Egypt, Strauss told reporters that the president called him twice yesterday to discuss "domestic matters." The first call came at 6:15 a.m. Washington time.