de Haas--van Alphen oscillations are observed in the alkaline-earth-metal subnitride ${\mathrm{NaBa}}_{3}\mathrm{N}.$ They are studied at various sample orientations with respect to the magnetic-field direction. A rich spectrum of quantum oscillation frequencies varying with the field orientation is found. The effective cyclotron masses of the carriers are found to depend on the area enclosed by the corresponding Fermi surface orbit, while the mean free path is constant over the whole Fermi surface. Four of the detected frequencies are attributed to two lens-shaped features of the Fermi surface, as computed with the tight-binding linear muffin-tin orbital method. Spin-orbit coupling is shown to play a crucial role in determining the topology of the respective orbits in reciprocal space. The experimental results and the computed electronic structure are discussed with regard to the void metal model for the subnitride.