Aligning active units ranging from bacteria through animals to drones often are subject to moving in a random environment; however, its influence on the emerging flows is still far from fully explored. For obtaining further insight, we consider a simple model of active particles moving in the presence of randomly distributed obstacles, representing quenched noise in two dimensions. Here we show that our model leads to rich behaviours that are less straightforwardly accessible by experiments or analytic calculations but are likely to be inherent to the underlying kinetics. We find a series of symmetry-breaking states despite the applied disorder being isotropic. For increasing obstacle densities, the system changes its collective motion patterns from (i) directed flow (ii) through a mixed state of locally directed or locally rotating flow to (iii) a globally synchronised rotating state, thereby the system violating overall chiral symmetry. Phase (iii) crosses over to a state (iv) in which clusters of locally synchronised rotations are observed. We find that if both present, quenched rather than shot noise dominates the behaviours, a feature to be considered in future related works.