I am self-studying Group Theory. I know that $A_{n}$ is a normal subgroup of $S_{n}$, but I've realized that I don't know another one, I mean, another subgroup of $S_{n}$ that is a normal subgroup of $S_{n}$. I would like to know if is known all the normal subgroups of $S_{n}$ and how many nonisomorphics of them there are in $S_{n}$, for all $n\geq 4$.
Thanks for your kindly help.