Using beta decays of a clean source of 12N produced at the IGISOL facility, we have measured the breakup of the 12C (12.71 MeV) state into three alpha particles with a segmented particle detector setup. The high quality of the data permits solving the question of the breakup mechanism of the 12.71 MeV state, a longstanding problem in few-body nuclear physics. Among existing models, a modified sequential model fits the data best, but systematic deviations indicate that a three-body description is needed.