Commentators here see cracks appearing in the political stronghold of former prime minister Kakuei Tanaka, who despite a conviction on bribery charges last year has remained a kingmaker in Japanese politics.

Just how serious the division is remains unclear. But analysts say it could alter the rules by which prime ministers have been selected in recent years and threaten the future of the incumbent, Yasuhiro Nakasone.

Tanaka commands the largest of five major factions in the ruling Liberal Democratic Party. His group can make or break prime ministers by lining up with smaller factions, as it has done for the past eight years and is now doing with Nakasone.

But an apparent split in the Tanaka ranks came to light during political maneuvering over Nakasone's efforts to gain renomination as party president. The post carries with it the prime ministership.

Nakasone won his new term, but not until he had dealt with an unexpected challenger, Susumu Nikaido, a 13-term member of the Diet, or parliament, who is the party's vice president and has admirers across factional and party lines.

Nikaido is also the number two man in the Tanaka faction.

Representatives of the anti-Nakasone forces appear to have met quietly with Nikaido in recent weeks to suggest that he run for the office. His candidacy also received backing from two minor middle-of-the-road parties.

Japanese newspapers reported that, just hours before Nakasone was due to be reconfirmed for a new term, Nikaido angrily told Tanaka that his group should not blindly back the incumbent. It should consider candidates from its own ranks, Nikaido reportedly said.

Neither man has offered a public account of what happened at the meeting, held at Tanaka's house in Tokyo's Mejiro district, although Nikaido has denied that he wanted the job for himself. But Tanaka's reputation as all-powerful was tarnished.

Leaders of the three factions that oppose the Nakasone-Tanaka alliance immediately picked up the ball. Nikaido, 75, could solve the party's unity problems, they argued, and he should be president. Their efforts died out in a day, at least partly, it appears, because Nikaido himself would not run.

Nikaido's motives remain a mystery. Some analysts speculate that he is anxious to make his mark as he reaches old age. Others point out that he is from Kagoshima prefecture, a region noted for its "men of action" in the feudal period.

Like Tanaka, Nikaido remains an influential man despite being tainted in the Lockheed payoff scandal of a decade ago. According to official prosecutors' reports, Nikaido was one of several Japanese officials who received money, but no charges were brought against him.

In December, a Tokyo court convicted Tanaka of accepting a payoff of $2 million from Lockheed during his tenure as prime minister in the early 1970s for helping arrange airplane sales.

Ignoring calls for his resignation, he has appealed the verdict and held onto his Diet seat from the rural prefecture of Nigata. Although he quit the Liberal Democratic Party, he continues to command its most powerful faction from his home.

How he manages to hang on is a subject of constant speculation in Japan. In some ways he is like a Tammany Hall boss, tough-talking and quick to play hard ball, but always certain to take care of his flock.

His clout is said to have brought unusual numbers of tunnels, dams and highways to his home district. His continuing appeal there was underlined in December when he won reelection with the highest number of votes received by any candidate in Japan.

Although Tanaka is politically unacceptable for another turn as prime minister, he is said to worry that putting in a younger man from his faction would undermine his own standing. The solution is Nakasone.

"We feel we get the best possible support from the Nakasone faction," said faction member Jushiro Komiyama.

Meanwhile, scourging "Tanakasone" remains standard fare in political speeches by the three other factions' leaders. Pressure mounted last year to the point that Nakasone pledged publicly to "eliminate the influence" of Tanaka in his government.

Nakasone never revealed how he would accomplish that in a Cabinet that included six members of the Tanaka faction. Later he appointed Nikaido to the vice president's post, a move that was viewed at the time as a further consolidation of Tanaka's influence.

Nakasone survived the challenge mounted by Nikaido, but his future will be in doubt if Tanaka can no longer deliver the votes. If Nikaido broke away and took some votes with him, Nakasone probably would be doomed as a viable candidate.

With these conflicts in mind, some commentators in Tokyo feel that the new Cabinet appointed by Nakasone will prove unstable. Some are now predicting elections, perhaps Nakasone's last, next year as the conflicts come out into the open.