They are from amongst the sects of the Raafidhah who affirmed their leadership (imaamah) to Ismaa’eel ibn Ja’far as-Saadiq, who was his eldest son.
It is said that he did not marry any woman and nor did he buy a slavegirl whilst his mother was alive, in accordance to the Sunnah of the Messenger of Allaah ﷺ with respect to Khadeejah (his first wife) and ‘Alee ibn Abe Taalib with respect to Faatimah (the daughter of the Prophet ﷺ).
There are differences of opinion as to his death whilst his father was alive; so some of them say that he died, whilst the benefit of of this is so that the imaamah could pass over to his children, particularly since it has been mentioned that it passed from Moosaa to Haaroon (‘alayhimaa as-salaam), then Haaroon died whilst Moosaa was still alive. So it is said that after Ismaa’eel, his son Muhammad ibn Ismaa’eel took the imaamah.
From amongst their most popular names is “al-Baatiniyyah” because they say that for every clear and present thing, there is a hidden and unseen, and for every revelation there is a meaning.
And they have many other names such as: “al-Qaraamitah” and “al-Mazdakiyyah”.