Transition metal dichalcogenides like 2H-NbSe_{2} in their two-dimensional (2D) form exhibit Ising superconductivity with the quasiparticle spins being firmly pinned in the direction perpendicular to the basal plane. This enables them to withstand exceptionally high magnetic fields beyond the Pauli limit for superconductivity. Using field-angle-resolved magnetoresistance experiments for fields rotated in the basal plane we investigate the field-angle dependence of the upper critical field (H_{c2}), which directly reflects the symmetry of the superconducting order parameter. We observe a sixfold nodal symmetry superposed on a twofold symmetry. This agrees with theoretical predictions of a nodal topological superconducting phase near H_{c2}, together with a nematic superconducting state. We demonstrate that in NbSe_{2} such unconventional superconducting states can arise from the presence of several competing superconducting channels.