If we tried the same thing with a non-normal subgroup, say the subgroup generated by the permutation (0 1 2), we would get something like Figure 20. It is clear from the lack of order in Figure 20 that there is a significant difference as compared to Figure 19. One cannot step back and mentally cluster Figure 20 by color and expect to obtain a valid multiplication table for a group of order 4; the colors are too mixed to permit this.