The structure of 58Fe was investigated at Gammasphere using 48Ca(13 ,14C,xn) fusion-evaporation reactions at a beam energy of 130 MeV. The level scheme has been revised and extended to J∼17 and an excitation energy of 16.6 MeV. Regular band structures consisting of low-energy ΔJ=1 transitions have been observed at moderate spin (J∼8-15) and are candidates for magnetic rotational bands. Self-consistent tilted-axis-cranking calculations within a relativistic mean-field theory were applied to investigate these bands and were found to reproduce the experimental results well. In other parts of the level scheme, quasirotational bands composed of stretched-E2 transitions have been extended to high spin, and other new bands have been identified. Positive-parity experimental states were compared to predictions of the spherical shell model using the GXPF1A, KB3G, and FPD6 effective interactions in the fp model space. The projected shell model, with a deformed quasiparticle basis including the neutron νg 9/2 orbital, was applied to interpret regular ΔJ=2 band structures that extend beyond the maximum spin available for π[(f 7/2) -2]- ν[(p 3/2f 5/2p 1/2)4] configurations and exhibit features characteristic of rotational alignment. It is clear that the νg 9/2 intruder orbital plays a crucial role in describing the quasirotational structures in this nucleus, even starting as low as J∼5. © 2012 American Physical Society.