Let $\phi : H \to Aut(N)$ be an action ($N,H$ are groups), and let $G = H \rtimes_\phi N$ be the semidirect product ($N$ is normal in $G$). I know that when $\phi$ is the action by conjugation, there is a ses $1 \to N \to G \to H \to 1$ with a section $ H \to G$. My question is
for a general $\phi$, is there also a ses $1 \to N \to G \to H \to 1$?