Within Shiism there are various sects that differ over the number of Imams, or path of succession. The issue of who is the rightful Imam has led to the growth of numerous sects within Shiism including: Ismailis (Seveners), Zaidis (Fivers), Alawites, Druze, and others.
Ithna Ashariya
According to the majority of Shia, or the Twelvers, the following is a listing of the rightful sucessors of Muhammad according to their beliefs. Each Imam was the son of the previous Imam, except for Husayn who was the brother of Hasan.
The Ismailis believe that the first six Imams listed above are the rightful sucessors of Muhammad, but differ beginning with the seventh, believing that Ismail bin Jafar was the rightful sucessor, and not his brother Musa al Kazim. From Ismail bin Jafar, the Ismaili line of Imams diverges to the descendents of Ismail, from whom the Aga Khans claim descent and their continuity. See [1] (http://www.amaana.org/history/history1.htm).
Zaidhiya (Zaidis)
The Zaidis believe that the first four Imams listed above are the rightful sucessors of Muhammad, but differ beginning with the fifth. The Zaidis believe that Zayd bin Ali, and not his brother Muhammad al Baqir was the rightful sucessor to the Imamate. The Imamate for Zaidis is thus transferred from Zayd bin Ali to the other Imams who followed him, they often took the title of caliph. Unusually, the Zaidi caliphate was not hereditary, although the caliph has to be descended from Ali.
External links
Graphical illustration of the Shia sects (http://philtar.ucsm.ac.uk/encyclopedia/islam/shia/index.html)
History of Imams from the "Aga Khani" point of view (http://www.amaana.org/history/history1.htm)
The Shi'aImam is considered by the Shi'a sect of Islam to be the rightful successor to Muhammad, and is similar to the Caliph in SunniIslam only with regards to the aspect of political leadership.
The majority Shia belief is that the Imams that God appointed, after the prophet Muhammad, were Ali, and eleven of his descendants from his wife, Fatima Zahra.
Each Imam was the son of the previous Imam, except for Husayn ibn Ali who was the brother of Hasan ibn Ali.