  Kinematical invariance groups of the 3d Schr\"odinger equations with position
dependent masses (PDM) and arbitrary potentials are classified. It is shown
that there exist 94 classes of such equations defined up to the generic
equivalence group, and 70 classes defined up to the equivalence groupoid. The
maximally extended kinematical invariance algebras of such equations appears to
be eight dimensional.
  The specific symmetries connected with the presence of the ambiguity
parameters are discussed and an extended class of systems which keep their
forms for arbitrary or particular changes of these parameters is specified.
  The exact solution of the selected PDM Schr\"odinger equation is presented.
This equation describes a deformed 3d isotropic harmonic oscillator and
possesses extended continuous symmetries and hidden supersymmetries with two
different superpotentials as well.
