Let $H$, $G_1$, $G_2$ be groups such that each $G_i$ $(i=1,2)$ has a subgroup $H_i$ isomorphic to $H$. Prove that the direct product $G_1 \times G_2$ has at least 3 distinct subgroups isomorphic to $H$.
I have zero idea how to approach this. I know that $H_1 \times H_2$ is subgroup isomorphic to $H$, but I don't know how to obtain the other two
EDIT: I now know that $H_1 \times H_2$ is wrong and that two groups that work are {$e_1$}x$H_2$, $H_1$x{e$_2$} are the other two, but I am unsure how to show that they are isomorphic to H since they are direct products. Is it enough to show f(uv)=f(u)f(v)