Dissociation of He-6 on a lead target has been studied at 240 MeV/u. The four-momenta of the two neutrons in coincidence with alpha-particles have been measured and used to reconstruct the three-body energy and angular correlations in the final state. For the first time, three-body correlations were included in the analysis of the He-6 dissociation data, and compared with calculations assuming a dipole mode for the electromagnetic dissociation. In addition, the experimental data have been analyzed using a series expansion of the final transition amplitude into hyperspherical functions, showing the importance of both nn and alpha n final-state interactions. It is shown that the dissociation process is governed by a transition of one neutron from the p-shell in the 6He ground state to the s-shell in the continuum further indicating that the role of the transition through an intermediate He-5(3/2(-)) state is more important than expected. (c) 2005 Elsevier B.V. All rights reserved.