A group, G, acting on a regular rooted tree has the congruence subgroup property (CSP) if every subgroup of finite index contains the stabilizer of a level of the tree. When the subgroup structure of G resembles that of the full automorphism group of the tree, additional tools are available for determining if G has the CSP.

In this talk, we look at the Hanoi towers group which has fails to have the CSP in a particular way. Then we will generalize this construction to a new family of groups and discuss the CSP for them.