Classifying all the group extension of $\mathbb{Z}_{n}$ by $\mathbb{Z}_{2}$ via the second cohomology group

Question

I want to find all the group extension $G$ of $\mathbb{Z}_{n}$ by $\mathbb{Z}_{2}$ up to equivalences. We know that for every extension $G$ there exists a factor set $f_{G}$, it is unique up to equivalences and it is a $2$-cocycle in $Z(\mathbb{Z}_{2},\mathbb{Z}_{n})\subseteq Hom_{\mathbb{Z}(\mathbb{Z}_{2})}(B_{2}(\mathbb{Z}_{2}),\mathbb{Z}_{n})$ where $B_{n}(\mathbb{Z}_{2})$ is a $\mathbb{Z}(\mathbb{Z}_{2})$-free module in the bar resolution of $\mathbb{Z}$. So every extension is associated with a class $[f_{G}]\in H^{2}(\mathbb{Z}_{2},\mathbb{Z}_{n})$. My question is to compute this cohomology group and from that deduce all the extensions.