Hi! I want to determine which of the subgropus of the symmetric group S(3) are normal. The condition is: for every g in G: g H g^-1 = H where H is a subgroup of G. I have determined all the subgroups of S(3) and I came up with 13. What I did after that is I considered 2 cases: 1: g is elem. of H, then g^-1 is also in H and the condition is satisfied. 2: g is not el. of H, but still el. of G, the same is true for g^-1. then I got stuck :( theoretically all the subgroups could be examined one by one, but it seems to me somehow too long and "not mathematical" Does anyone know a better way? thanks in advance! ° and another question: If H is a normal subgroup of G, what should one understand under "G modulo H"