We have observed various symmetry properties of the Raman heterodyne signals of spin echoes of Pr-141 nuclei in Pr3+:LaF3 and explained them. We have theoretically derived a general symmetry law that governs the symmetry property of the signals for the static magnetic-field reversal. Observed symmetry properties could be explained by using this law and the nature of the product of three matrix elements relevant to the Raman heterodyne process. In some cases the symmetry properties could be explained only from a consideration of the geometrical symmetry of the system. Numerical calculations were performed under some assumptions on the optical pumping and the effect of level multiplicity, and the results qualitatively support the explanation of observed symmetry properties. Several symmetry properties that have not been observed are predicted.