  A Grigorchuk-Gupta-Sidki (GGS-)group is a subgroup of the automorphism group
of the $p$-adic tree for an odd prime $p$, generated by one rooted automorphism
and one directed automorphism. Pervova proved that all torsion GGS-groups do
not have maximal subgroups of infinite index. Here we extend the result to
non-torsion GGS-groups, which include the weakly regular branch, but not
branch, GGS-group.
