Solution
= Solution
\b[False.] Let $G=C_4$ and $H=C_2\times C_2$, and in each choose a <subgroup> of order two. Then the chosen normal <subgroups> are isomorphic and both quotients are $C_2$, while $G$ and $H$ are not isomorphic.
= Solution
\b[False.] Let $G=C_4$ and $H=C_2\times C_2$, and in each choose a <subgroup> of order two. Then the chosen normal <subgroups> are isomorphic and both quotients are $C_2$, while $G$ and $H$ are not isomorphic.