  We discuss the maximum kinematical invariance group of the quantum harmonic
oscillator from a view point of the Ermakov-type system. A six parameter family
of the square integrable oscillator wave functions, which seems cannot be
obtained by the standard separation of variables, is presented as an example.
The invariance group of generalized driven harmonic oscillator is shown to be
isomorphic to the corresponding Schroedinger group of the free particle.
