Maximal subgroups of a family of iterated monodromy groups
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 ≥ 2. A larger family of groups, which contains these generalised Basilica groups, is
