The number of isomorphism classes for the symmetry group of 6 elements?

Question

The different isomorphism classes of subgroups of $S_3$ is:
trivial, $Z_2$, $Z_3$ and $S_3$ itself - that is $4$ different types

The number of isomorphism classes of subgroups of $S_4$ is $9$ and $S_5$ is $16$.

Do anyone know this number for $S_6$?

Answer 1

As so often OEIS has the answer:

http://oeis.org/A174511

There are exactly 29 isomorphism types of subgroups of $S_6$.