We examine inclusions of C ^*-algebras of the form A^H ⊆ A Ì_r G, where G and H are groups acting on a unital simple C ^*-algebra A by outer automorphisms and H is finite. It follows from a theorem of Izumi that A^H ⊆ A is C ^*-irreducible, in the sense that all intermediate C ^*-algebras are simple. We show that A^H ⊆ A Ì_r G is C ^*-irreducible for all G and H as above if and only if G and H have trivial intersection in the outer automorphisms of A, and we give a Galois type classification of all intermediate C ^*-algebras in the case when H is abelian and the two actions of G and H on A commute. We illustrate these results with examples of outer group actions on the irrational rotation C ^*-algebras. We exhibit, among other examples, C ^*-irreducible inclusions of AF-algebras that have intermediate C ^*-algebras that are not AF-algebras; in fact, the irrational rotation C ^*-algebra appears as an intermediate C ^*-algebra.