We have studied the structures and misorientation angles of subgrains in large single-grain REBa2Cu3Oy (RE = Y, Sm, Nd) bulk superconductors by polarized optical microscopic observations and pole-figure measurements combined with micro-area X-ray diffraction analyses. We have found that subgrains were more elongated along the crystal growth direction with increasing misalignment, and that misorientation angles of the subgrains were almost comparable with those previously obtained on similar materials. We also discuss the possible mechanism for the subgrain formation.