The heavy-ion radiative capture reaction, C12(C12,γ), has been investigated at energies both on- and off-resonance, with a particular focus on known resonances at Ec.m.=6.0, 6.8, 7.5, and 8.0 MeV. Gamma rays detected in a BGO scintillator array were recorded in coincidence with Mg24 residues at the focal plane of the DRAGON recoil separator at TRIUMF. In this manner, the relative strength of all decay pathways through excited states up to the particle threshold could be examined for the first time. Isovector M1 transitions are found to be a important component of the radiative capture from the Ec.m.=6.0 and 6.8 MeV resonances. Comparison with Monte Carlo simulations suggests that these resonances may have either J=0 or 2, with a preference for J=2. The higher energy resonances at Ec.m.=7.5 and 8.0 MeV have a rather different decay pattern. The former is a clear candidate for a J=4 resonance, whereas the latter has a dominant J=4 character superposed on a J=2 resonant component underneath. The relationship between these resonances and the well-known quasimolecular resonances as well as resonances in breakup and electrofission of Mg24 into two C12 nuclei are discussed.