what are the subgroups of $\mathbb{Z}_2 \times \mathbb{Z}_{12}$ of order $6$? I know that there are three such subgroups, and two subgroups are clear to me, namely the subgroup isomorphic to $\mathbb{Z}_6$ and the subgroup isomorphic to $\mathbb{Z}_2\times \mathbb{Z}_3$. But I can't see the other one. Please help!
Subgroups of $\mathbb{Z}_2 \times \mathbb{Z}_{12}$ of order $6$
8
$\begingroup$
abstract-algebra
group-theory
finite-groups
abelian-groups