  The problem of group extension can be divided into two sub-problems. The
first is to find all the possible extensions of $H$ by $K$. The second is to
find the different ways a group $G$ can arise as an extension of $H$ by $K$.
Here we prove that the direct product $H\times K$ can arise as an extension of
$H$ by $K$ in an essentially unique way: that is the direct extension. I would
like to thank Yacine Dolivet for drawing my attention to the direct ``extension
theorem'', and Anne-Marie Aubert as well as Charles-Antoine Louet for their
support.
