The Fatimid dynasty always tried to combine pragmatic secular rule with idealistic religion. The Caliph/Imam was not only the war leader and ruler, he was also the holiest descendant of Ismail.
We’ve already seen one major split among Ismaili fanatics, when the Vizier Afdal promoted younger brother Musta’ali over heir apparent Nizar. During the 12th century, the Nizari Ismailis were mostly in Persia, trying to rebel against Baghdad’s Turkish rule. These Nizaris even took the radical step of composing their holy writings in Persian, not in Arabic.
But in 1132, another split began.
Most Muslims in Egypt accepted Musta’ali’s rule pragmatically, but some believed fervently that the choice of Musta’ali had also been idealistic and holy. When this Imam died, his son al-Amir became Imam after him, so all was still well. In 1130, the birth of an heir-apparent son named Tayyib was celebrated in Cairo. But in 1132, the Caliph-Imam was assassinated. The heir, Tayyib, was no more than two years old.
Hafiz, a half-brother to the dead Caliph, became Regent for baby Tayyib. This kind of plan usually worked out badly in those times. Within a short time, Hafiz declared himself Caliph-Imam, since he too was a son of the previous one. Vizier Afdal and everyone who had charge of baby Tayyib were suddenly assassinated. The Nizari Assassins were a convenient scapegoat, but it’s just as likely that Hafiz merely paid his own killing team. Tayyib vanished from history, first with a legend of being hidden like Moses in a basket, carried to a mosque for safe-keeping. Then, since he was the true Imam even at this young age, he went into “occultation,” the hidden state where true Imams await their future revealing.
Ismailis in Yemen never accepted Hafiz; they were partisans of Tayyib. This was the next big split among Shi’ites: Tayyibi and Hafizi. Hafizi partisans didn’t have a long run, though; the descendants of Hafiz definitely died out, without occultation or mystery, within a few generations. Remaining Hafizi believers made amends to the Tayyibis and just joined them. There is still a Tayyibi Ismaili Shi’ite sect in Yemen.
During the last years of the Hafizis in Cairo, their Vizier tried to solve the three-way power problem by allying with the Crusader Kingdoms against the growing power of Zengi and his heirs. It was the last stand for Arab rule. Turks and Kurds now held Baghdad, Damascus, and much of Persia; they were taking more and more of Anatolia. However much the last Hafizis might be rejected by Tayyibis and Nizaris, they were undisputed as descendants of Ismail, who was a descendant of Mohammed. If these last Fatimids, fractured by idealistic splits, could not hold onto power against the Turks and Kurds, Arab aristocracy was basically over.
Spoiler: As we know, Arab political power only revived in the 20th century, after the First World War, fittingly by means of another “Crusader” alliance. By then, Turkish power had gone through its own cycles of division and decay.