Systematic studies by powder neutron diffraction of the magnetic phases in rare earth-indium compounds within the AuCu3-type cubic structure are presented. All the magnetic structures are described, at any temperature with propagation vectors from the [1/2, 1/2, 0] star. The analysis of the intensities shows that the magnetic structures are very likely multiaxial. The case of NdIn3 appears very puzzling as its three magnetic phases remain indistinguishable by powder neutron diffraction. In addition to the crystalline electric field and the Heisenberg-type exchange interactions, antiferroquadrupolar interactions appear as responsible of the stabilization process of these multiaxial structures.