LaNiGa2 is superconductor that has been shown to break time-reversal symmetry in the superconducting state without any known nearby magnetism. Recently, single crystals of LaNiGa2 have been synthesized, revealing a nonsymmorphic Cmcm space group. Here, we report on measurements of the electronic structure of LaNiGa2 throughout the three-dimensional Brillouin zone (BZ) using angle-resolved photoemission spectroscopy. Our findings show broad consistency with density functional theory calculations and provide evidence for degeneracies in the electronic structure that are predicted from the space group symmetry. We report evidence for those predicted symmetry-enforced degeneracies as well as accidental near degeneracies throughout the BZ. These degeneracies and near degeneracies may play a role in the pairing mechanism of LaNiGa2. Our results provide insight into the interplay between structure, fermiology, and superconductivity in unconventional superconductors with nonsymmorphic space group.