They weren't successful in exterminating the natives. Later on Joe Stalin shipped them to Siberia but again the Russians failed to exterminate them. More recently the Chechnyans have managed to "break away".
I think Islam is a secondary issue with these people.
The new leader of Chechnya is about nothing but Islam.
http://islaminaction08.blogspot.com/2009/03/russiaislamic-law-allowed-in-chechnya.html