Let G be a semisimple simply connected algebraic group defined and split over the field F p with p elements, G(F q ) be the finite Chevalley group consisting of the F q -rational points of G where q=p r , and G r be the rth Frobenius kernel of G. This paper investigates relationships between the extension theories of G, G(F q ), and G r over the algebraic closure of F p . First, some qualitative results relating extensions over G(F q ) and G r are presented. Then certain extensions over G(F q ) and G r are explicitly identified in terms of extensions over G.