In this paper, we study a registration problem that is motivated by a practical biology problem - fitting protein structures to low-resolution density maps. We consider registration between two sets of lines features (e.g., helices in the proteins) that have undergone not a single, but multiple isometric transformations (e.g., hinge-motions). The problem is further complicated by the presence of symmetry in each set. We formulate the problem as a clique-finding problem in a product graph, and propose a heuristic solution that includes a fast clique-finding algorithm unique to the structure of this graph. When tested on a suite of real protein structures, the algorithm achieved high accuracy even for very large inputs containing hundreds of helices.