We investigate triple nodal points, i.e., three-fold degeneracies of energy bands in the momentum space of three-dimensional crystalline solids. First, based on the symmetries required for their stability, we develop a classification of triple nodal points in weakly spin-orbit-coupled materials. Second, by combining the derived classification with symmetry indicators for corner charges, we find that pairs of triple points in semimetals are associated with monopole charges and higher-order topology. The higher-order bulk-boundary correspondence of such triple-point pairs is a quantized fractional jump in the momentum dependence of the electric charge localized at the crystal hinges. I will illustrate these results using first-principles calculations for the compound Sc$_3$AlC in applied strain.