We study the effect of magnetic field on the nonequilibrium transport properties of a general cubic quantum network described by a tight-binding Hamiltonian. We demonstrate that the symmetry of open systems can be manipulated by the direction of the magnetic field. Starting with all the symmetries preserved in absence of a field, the anisotropic and isotropic field systematically break the symmetries, influencing all nonequilibrium properties. For square and cubic structure, we are able to identify the steady states that comprise of pure states, bath-dependent states (nonequilibrium steady states), and also nonphysical states. As an application, we show numerically for large cubic networks that the symmetry breaking can control nonequilibrium currents and that different environmental interactions can lead to novel features which can be engineered in artificial super-lattices and cold atoms.