this what i got

G =S,andH = A, ,|Is H anormal subgroup of G. Step1: Understand the Groups e ,: The symmetric group on 4 elements. It has 41 = 24 elements. e A,: The alternating group on 4 elements (even per mutations in S,). It has 12 elements. Step2: Is A, a sub of $,? The are twelve elements in Ay The group A, is subgroup of S, because A, (1) (1 2)(34) (13)(24) (1 4)(23) (123) (132) (124) (142) (134) (143) (234) (243)