Let $K_4$ be the Klein $4$-group and let $C_2$ be the cyclic group of order $2$.
Suppose I know that $K_4 \cong G/C_2$ for some group $G$. Is $G$ unique, and if so, how can I determine what $G$ is?
I know that a possible group $G$ is the quaternion group, but I don't know how to show it.