Detailed theoretical studies of the electronic structure of (InGa)(AsSb)/GaAs/GaP quantum dots are presented. This system is unique since it exhibits concurrently direct and indirect transitions both in real and momentum space and is attractive for applications in quantum information technology, showing advantages as compared to the widely studied (In,Ga)As/GaAs dots. We proceed from the inspection of the confinement potentials for k = 0 and k = 0 conduction and k = 0 valence bands, through the formulation of k · p calculations for k-indirect transitions, up to the excitonic structure of Γ-transitions. Throughout this process we compare the results obtained for dots on both GaP and GaAs substrates, enabling us to make a direct comparison to the (In,Ga)As/GaAs quantum dot system. We also discuss the realization of quantum gates.