The structure of 133La has been investigated using the 116Cd(22Ne ,4pn) reaction and the Gammasphere array. Three new bands of quadrupole transitions and one band of dipole transitions are identified and the previously reported level scheme is revised and extended to higher spins. The observed structures are discussed using the cranked Nilsson-Strutinsky formalism, covariant density functional theory, and the particle-rotor model. Triaxial configurations are assigned to all observed bands. For the high-spin bands it is found that rotations around different axes can occur, depending on the configuration. The orientation of the angular momenta of the core and of the active particles is investigated, suggesting chiral rotation for two nearly degenerate dipole bands and magnetic rotation for one dipole band. It is shown that the h11/2 neutron holes present in the configuration of the nearly degenerate dipole bands have significant angular momentum components not only along the long axis but also along the short axis, contributing to the balance of the angular momentum components along the short and long axes and thus giving rise to a chiral geometry.