I'm trying to solve a problem from my Group Theory course. It goes like this:
Being $S_n$ the symmetric group of order $n$. Find the number of index 2 subgroups of $S_n$.
I'm not pretty sure how to start. I guess it would have something to do with the normal subgroups of $S_n$, since any index two subgroup of a group $G$ is normal to $G$. But I don't know how to compute this number of subgroups, I just know that $|S_n|=n!$. Any help will be appreciated.