The directed assembly of shape anisotropic magnetic particles into targeted macrostnictures requires judicious particle design. We present a framework to understand the self-assembly of magnetic non-Brownian H-shaped particles and the formation of branched networks under an applied magnetic field. A finite element integration (FEI) method is developed to identify the preferred particle orientation (relative to the applied field) at different values of the geometric parameters defining H shapes, and used to construct a phase diagram to generalize the results. Theoretical predictions are validated by comparing with experiments performed using magnetic hydrogels synthesized using stop-flow lithography (SFL). We demonstrate the ability of H-shaped particles to form chains parallel to the field that can thicken in a direction orthogonal to the field, and in some cases with branching. The assembly of a suspension containing H-shaped particles, or rods, or a combination of both, is reported.