Flow coefficients v_{n} of the orders n=1-6 are measured with the High-Acceptance DiElectron Spectrometer (HADES) at GSI for protons, deuterons, and tritons as a function of centrality, transverse momentum, and rapidity in Au+Au collisions at sqrt[s_{NN}]=2.4 GeV. Combining the information from the flow coefficients of all orders allows us to construct for the first time, at collision energies of a few GeV, a multidifferential picture of the angular emission pattern of these particles. It reflects the complicated interplay between the effect of the central fireball pressure on the emission of particles and their subsequent interaction with spectator matter. The high precision information on higher order flow coefficients is a major step forward in constraining the equation of state of dense baryonic matter.