# Asymptotics of the number distinct of subgroups of $S_n$ as $n$ goes to infinity [duplicate]

I would like to have a sense of the number of distinct subgroups (that is, isomorphic subgroups are counted multiple times) the symmetric group $S_n$ has as $n$ goes to infinity. I suspect nailing down the exact number is harder than understanding the general size. Can someone help me understand this?