Abstract Algebra: Find a number of non-isomorphic subgroup of $S_3$

Question

I'm having difficulty in understanding the method to find the solution for this question.

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Question: Find the number of non-isomorphic subgroup of $S_3$

So is this the way to find the number of non-isomorphic subgroups of $S_3$? Since $S_3=\{1,(123),(132),(12),(23),(13)\}$, there are six non-isomorphic subgroups of $S_3$.

Answer 1

Since $S_3$ has order $6$, its subgroups must have order $1$, $2$, $3$ or $6$. Groups of order $1$, $2$, $3$ are all cyclic. So there are $4$ non-isomorphic subgroups of $S_3$.