  We extend to the context of algebraic groups a classic result on extensions
of abstract groups relating the set of isomorphism classes of extensions of $G$
by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof
should be easily generalizable to other contexts. We also study the subset of
classes of split extensions and give a quick application by proving a
finiteness result on these sets over a finite field.
