The largest North Caucasian peoples are Chechens (800,000), and Avars (500,000). Some of the North Caucasian peoples possess their autonomous republics within the Russian Federation: Adyghe (Adygea), Cherkess (Karachay-Cherkessia), Kabardins (Kabardino-Balkaria), Ingush (Ingushetia), Chechens (Chechnya), while Northeast Caucasian peoples mostly live in Dagestan. Abkhazians live in Abkhazia, which is de facto independent, but de jure is autonomous republic within Georgia.
References
Mile Nedeljković, Leksikon naroda sveta, Beograd, 2001.