Mustaali
The Mustaali recognized as the rightful Imams:
19. Aḥmad al-Mustaʿlī, (son of Abū Tamīm Ma'add al-Mustanṣir bi-llāh), 9th Fatimid Caliph, died 1101.
20. Al-Āmir bi-Aḥkāmillāh, son of al-Mustaʿlī, 10th Fatimid Caliph, died 1130.
Hafizi Muslims claim that Amir died without an heir and was succeeded as Caliph by his cousin Al-Hafiz. The Mustaʿlī split into the Hafizi, who accepted him and his successors as Imam, and the Tayyibi, who believed that Amir's purported son At-Tayyib was the rightful Imam and had gone into occultation:
Read more about this topic: List Of Ismaili Imams