Yes there was a serious split in early Islam which did result in the Sunni - Shi'ite split that continues today. After Muhammad died in 632 AD, Muslims had difficulty choosing his successor, whom they would call the Caliph. The Shia believed that the rule should stay within the family of the prophet. Initially a peaceful settlement was reached and Abu Bakr, Muhammad's father-in-law and one of his earliest and wealthiest converts was chosen as leader. Bakr was a strong leader and the Muslims began to expand outside of the Arabian Peninsula. It was not long before the problems of succession flared up again and at the death of the fourth caliph, Uthman. This time the competitors for the caliphate included Ali, the grandson of Muhammad by his daughter, Fatima, and Muawiya, the governor of Syria as well as Uthman's cousin, and an enemy of Ali. Ali was assassinated and Muawiya became Caliph. Ali's son, Hussein continued the fight for the Shia until he too was killed and beheaded. The Shia never accepted the authority of the Caliph and elected their own leader whom they call the Iman. Those who accepted Muyawiya as leader became called the Sunni. The split between the two branches remains today.
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When Muhammad died he did not leave a successor. A power struggle over how to choose a successor erupted.
Many felt that the new leader should be elected while others felt a new leader should be chosen by heredity.
Muslim sects included in this struggle are the Sunnis, Shi'a, and the Sufi.
(the link below offers a timeline of Islamic history)