The degeneracy of d-orbitals in an atom depends on the environment in which the atom is present. In a free atom all the five d-orbitals in a subshell are degenerate. In a magnetic field, however, degeneracy is lost.

If the atom is part of a molecule, as,say , the central atom in a transition metal complex, the degeneracy of d-orbitals depends on the geometrical arrangement of ligands around the central atom. In the common cases of tetrahedral and octahedral complexes , the five d-orbitals are split into two sets t2 and e in the former and t2g and EG in the latter. The orbitals in the t2 or t2g sets are triply degenerate while those in the e or eg are doubly degenerate. Remember that a slight distortion in the ideal geometry CHANGES the SPLITTING pattern somewhat. A tetragonal distortion of a regular octahedral complex removes the degeneracy of the dz^2 and dx^2-y^2 orbitals as also of dxy and dxz, dyz. Degeneracy of d-orbitals is also subject to the Jahn Teller effect in NONLINEAR complexes.

For the splitting of d-orbitals in other geometries please look into a good Inorganic Chemistry textbook, e.g., Coordination Chemistry by D Bannerjea or Inorganic Chemistry by Huheey.