Magnetic torque measurements have been performed to investigate the phase transitions of the metallic pyrochlore compound Cd2Re2O7, in which a spin-orbit (SO) interaction leads to unique multipole orders associated with an inversion symmetry breaking. We find that the magnetic torque signals with a fourfold symmetry (τ4- H4) as well as a twofold symmetry (τ2- H2) are significantly enhanced at low temperatures below a structural phase transition temperature (∼200 K). The analyses of the torque curve symmetries show that the τ4 term arises from an even-parity order parameter (OP) with the irreducible representation Eg, whereas the τ2 term from an odd-parity OP with Eu, T1u or T2u. The parity mixing of the primary OPs shows a peculiar phase transition in the SO coupled Cd2Re2O7. The coexistence of the two OPs provides important insights into the origin of the multipole orders induced by the SO interaction.