Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
266 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×Dic12 | C2 | semidirect |
| 4. C3×#818 | C2 | semidirect |
| 5. #63565 | C2 | semidirect |
| 19. C2×Dic12 | D3 | semidirect |
| 26. #818 | D3 | semidirect |
| 65. C2×C3⋊D3 | Q16 | semidirect |
| 143. C32 | #467 | semidirect |
| 177. C3 | #4887 | semidirect |
| 178. C3 | #5188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D3 | 2 |
| C2×C3×Dic12 | 2 |
| #63871 | 2 |
| C3×#818 | 2 |
| #63565 | 2 |
| #5188 | 3 |
| #4887 | 3 |