  Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi
Class A cosmologies. In particular, we consider General Relativity, minimally
coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the
approach. Several invariant solutions are determined and classified according
to the form of the scalar field potential. The approach gives rise to a
suitable method to select classical solutions and it is based on the first
principle of the existence of symmetries.
