  We investigate the class $\mathcal{MN}$ of groups with the property that all
maximal subgroups are normal. The class $\mathcal{MN}$ appeared in the
framework of the study of potential counter-examples to the Andrews-Curtis
conjecture. In this note we give various structural properties of groups in
$\mathcal{MN}$ and present examples of groups in $\mathcal{MN}$ and not in
$\mathcal{MN}$.
