What are the different factions in Islam and how do their beliefs differ?

For the record, God never supported dividing into different factions. In fact, He discourages this division of His religion. Some of the groups you asked about are: the Sunni, the Shia, the Ismailis, the Ahmadiyas, the Sufis, the Wahhabis, the Alawis, the Druze, the Kharjites, the Zaydis, and the Nation of Islam. These factions were either born of political differences, or were organized by leaders who decided that their religious interpretations were the most guided. Thus, the followers were compelled to break from the broader and more general religious practice prescribed in the Quran. Because of these issues, a group of Muslims have emerged who just observe Submission to God alone.