Is there any groups that have split from the orthodox church?

Yes, there are groups that split from the Eastern Orthodox Church. The so called "Nestorians," now known as the Church of the East, or the Assyrian Church of the East; the so-called "Monophysites," now known as the Armenian Apostolic Church, the Syrian Orthodox Church, The Malankara Church, the Ethiopian Tewahedo Church, the Coptic Church, and the Eritrean Orthodox Church; the Roman Catholic Church. All of these "splits" resulted in new organizations that have never reconciled completely with the Orthodox Churches.

Also, splits more "within" the Orthodox Church that have been reconciled in some cases, and not in other cases (some small groups believe they they alone carry on the Orthodox Church, and that the current Orthodox Churches are no longer Orthodox) Old Rite or Old Believers, Old Calendarists (several different organizations), Catacomb Church in Russia (which is virtually extinct; new varieties seem to come into existence frequently).

Nationalist driven splits-the Ukrainian Orthodox Church is the only large grop that insists on being on its own, while its Mother Church, the Russian Orthodox Church, does not sanction the unilateral declaration of "independence," as that is not how is has been traditionally done within the Church.