The stannide family of materials A3T4Sn13 (A = La,Sr,Ca, T = Ir,Rh) is interesting due to the interplay between a tunable lattice instability and phonon-mediated superconductivity with Tc ~ 5-7 K. In Sr3Ir4Sn13 a structural transition temperature T* ~ 147 K associated with this instability has been reported, which is believed to result from a superlattice distortion of the high temperature phase on cooling. Here we report the first experimental study of the electronic structure of a member of this material family - Sr3Ir4Sn13 through measurements of quantum oscillations and comparison with density functional theory calculations. Our measurements reveal good agreement with theory using the lattice parameters consistent with a body-centred cubic lattice of symmetry I-43d of the low temperature phase. The study of the fermiology of Sr3Ir4Sn13 we present here should help inform models of multiband superconductivity in the superconducting stannides.