For n ≥ 5, the alternating group A n is simple, and the induced quotient is the sign map: A n → S n → S 2 which is split by taking a transposition of two elements. Thus S n is the semidirect product A n ⋊ S 2, and has no other proper normal subgroups, as they would intersect A n in either the identity (and thus themselves be the identity or a 2-element group, which is not normal), or in A n (and thus themselves be A n or S n).