How many subgroups of order 6 are in $S_6$?
I have been thinking on first counting the number of elements of order $6$ in $S_6$. Also, I have in mind using the fact the a group of order 6 is either isomoporhic to $S_3$ if its non abelian or to $Z_6$ if abelian. Do these facts help? Does someone have a better approach?