Originally Posted by

**Deveno** (up to isomorphism)

$\displaystyle 1\longrightarrow \mathbb{Z}_4 \longrightarrow^{\!\!\!\!\!\!\!\!\!\beta}\ \, G \longrightarrow^{\!\!\!\!\!\!\!\!\!\alpha}\ \, \mathbb{Z}_2 \longrightarrow 1$

$\displaystyle \mathbb{Z}_2\longrightarrow^{\!\!\!\!\!\!\!\gamma} \ \, G$

$\displaystyle \gamma \circ \alpha = 1_{\mathbb{Z}_2}$

(if my latex were better i'd try to put it all on one line, this is a right-split short exact sequence).

if so, is there a "smaller" diagram which conveys the same information?