Symmetric Group on 3 Letters/Subgroups

Subgroups of the Symmetric Group on $3$ Letters
Let $S_3$ denote the Symmetric Group on $3$ Letters, whose Cayley table is given as:

The subsets of $S_3$ which form subgroups of $S_3$ are:
 * $S_3, \set {e, \tuple {123}, \tuple {132} }, \set {e, \tuple {12} }, \set {e, \tuple {13} }, \set {e, \tuple {23} }, \set e$