Clans and The Caliphate
After the introduction of Islam, the Quraysh gained supremacy and produced the three dynasties of the Ummayad Caliphate, the Abbasid Caliphate and the Fatimid Caliphate. The split between the Shi'a and Sunni branches of Islam centers over the succession to Muhammad. The Sunnis believe Abu Bakr was elected as Muhammad's successor while the Shi'a (literally "companions ") believe Muhammad appointed Ali ibn Abi Talib as his successor.
Ali was a member of Muhammad's clan, the Banu Hashim. Abu Bakr, while a close companion of Muhammad, came from the Banu Taym clan.
The second caliph, Umar ibn al-Khattab, was from the Banu Adi clan.
The third caliph, Uthman ibn Affan, was from the Banu Umayyah clan.
When Ali was made caliph after the death of Uthman, the Caliphate was in the hands of the Banu Hashim, but he was almost immediately challenged by Muawiyah, who was a member of the Umayyad clan. After Ali's assassination at the hands of the Kharajites, the Shi'a hoped his son Hasan would become Caliph, but he was forced to defer to Muawiyah, who, in violation of the treaty signed with Hasan bin Ali, established the Umayyad line of Caliphs.
After the death of Muawiyah, his son Yazid became caliph but was almost immediately challenged by Ali's younger son, Hussayn. Hussayn would not swear allegiance to Yazid for disgracing Islam by various heinous acts, among those the alleged corruption of Yazid and Hussayn's acknowledgment of the caliphate's non-hereditary lineage, which Yazid had breached. Hussayn was martyred by the stronger forces of Yazid at the Battle of Karbala. This event would ultimately lead to a full schism between Shi'a Islam and Sunni Islam.
In the Shi'a view Muhammad's descendants through Ali were persecuted by Umayyad Caliphs which did not help matters.
Read more about this topic: Quraysh Tribe