  The Basilica group is a well-known 2-generated weakly branch, but not branch,
group acting on the binary rooted tree. Recently a more general form of the
Basilica group has been investigated by Petschick and Rajeev, which is an
$s$-generated weakly branch, but not branch, group that acts on the $m$-adic
tree, for $s,m > 1$. A larger family of groups, which contains these
generalised Basilica groups, is the family of iterated monodromy groups. With
the new developments by Francoeur, the study of the existence of maximal
subgroups of infinite index has been extended from branch groups to weakly
branch groups. Here we show that a subfamily of iterated monodromy groups,
which more closely resemble the generalised Basilica groups, have maximal
subgroups only of finite index.
