A complete kinematic measurement of the 6 Li( 3 He, 3 H)αpp reaction is performed at E lab = 50 MeV, to investigate the cluster structure of 6 Be. The energy and angular distributions of the breakup particles, emitted from the ground and first excited states of 6 Be, are compared to three-body resonance and two-body sequential decay calculations. The results indicate a rather pure three-body configuration of the 2 + state of 6 Be but they are not conclusive regarding the decay mode of the 0 + state. No branching ratio between sequential and three-body decay paths could be extracted. Excitations above the 2 + state were populated at E x = 1.67-23 MeV. Decay through 5 Li-p and 2 He-4 He channels is identified in the continuum of 6 Be, and the reaction mechanism is discussed.