= Solution
Use additive notation and take $G=\mathbb Z/4\mathbb Z$, $N=\{0,2\}$. Its <quotient group> is $C_2$. A <group homomorphism> from $C_2$ sends its generator to an element annihilated by $2$, so the image must be either $0$ or $2$. Both project to the identity coset $N$, and neither can project to the nonidentity generator of $G/N$. Therefore \b[this quotient projection has no homomorphic section]. It is a nonsplit <group extension>, despite both $G$ and $N$ being nontrivial finite <groups>.
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