Hydrides are present in the reduced states of the iron-molybdenum cofactor (FeMoco) of Mo nitrogenase and are believed to play a key mechanistic role in the dinitrogen reduction reaction catalyzed by the enzyme. Two hydrides are present in the E4 state according to 1H ENDOR and there is likely a single hydride in the E2 redox state. The 2-hydride E4 state has been experimentally observed to bind N2 and it has been speculated that E3 may bind N2 as well. However, the E3 state has not been directly observed and very little is known about its molecular and electronic structure or reactivity. In recent computational studies, we have explored the energy surfaces of the E2 and E4 by QM/MM modelling, and found that the most stable hydride isomers contain bridging or partially bridging hydrides with an open protonated belt sulfide-bridge. In this work we systematically explore the energy surface of the E3 redox state, comparing single hydride and two-hydride isomers with varying coordination and bridging vs. terminal sulfhydryl groups. We also include a model featuring a triply protonated carbide. The results are only mildly dependent on the QM-region size. The three most stable E3 isomers at the r2SCAN level of theory have in common: an open belt sulfide-bridge (terminal sulfhydryl group on Fe6) and either 2 bridging hydrides (between Fe2 and Fe6), 1 bridging-1-terminal hydride (around Fe2 and Fe6) or a dihydrogen ligand bound at the Fe2 site. Analyzing the functional dependency of the results, we find that functionals previously found to predict accurate structures of spin-coupled Fe/Mo dimers and FeMoco (TPSSh, B97-D3, r2SCAN, and B3LYP*) are in generally good agreement about the stability of these 3 E3 isomers. However, B3LYP*, similar to its parent B3LYP method, predicts a triply protonated carbide isomer as the most stable isomer, an unlikely scenario in view of the lack of experimental evidence for carbide protonation occurring in reduced FeMoco states. Distinguishing further between the 3 hydride isomers is difficult and this flexible coordination nature of hydrides suggests that multiple hydride isomers could be present during experimental conditions. N2 binding was explored and resulted in geometries with 2 bridging hydrides and N2 bound to either Fe2 or Fe6 with a local low-spin state on the Fe. N2 binding is predicted to be mildly endothermic, similar to the E2 state, and it seems unlikely that the E3 state is capable of binding N2.