Let $S_n$ denote the symmetric group on $n$ symbols. The group $S_3\oplus(\Bbb Z/2\Bbb Z)$ is isomorphic to which of the following groups?
1.$\Bbb Z/12\Bbb Z$
2.$\Bbb Z/6\Bbb Z \oplus \Bbb Z/2\Bbb Z$
3.$ A_4$, the alternating group of order $12$
4.$ D_6$ the dihedral group of order $12$.
I can easily discard option 1st and 2nd. Since $S_3$ is non abelian implies $S_3\oplus(\Bbb Z/2\Bbb Z)$ s non abelian. But I have problem to deal with other options. Will be pleased if you share your valuable knowledge.