We demonstrate the control of the mode degeneracy when a liquid crystal (LC) is infiltrated into an InGaAsP membrane photonic crystal nanocavity with embedded InAs quantum dots. Mode splitting exists in the anisotropic nematic LC state, and not in the unfilled or isotropic LC state. The degeneracy lifting of the quadrupole mode is attributed to the different interactions of the two orthogonal basis modes of the degenerate mode with the two components of the refractive index of the LC. The interpretation is supported by the quantitative agreement between the experimental results and the three-dimensional finite-difference time-domain computations.