Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 1. C2×C8×C3⋊D3 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. #63916 | C2 | semidirect |
| 4. C3×#818 | C2 | semidirect |
| 5. #63562 | C2 | semidirect |
| 19. C2×D24 | D3 | semidirect |
| 26. #818 | D3 | semidirect |
| 38. C32×C8 | D4 | semidirect |
| 66. C2×C3⋊D3 | D8 | semidirect |
| 105. C3×C8 | D12 | semidirect |
| 106. C3×C8 | #67 | semidirect |
| 153. C32 | #466 | semidirect |
| 165. C8 | #626 | semidirect |
| 192. C3 | #4883 | semidirect |
| 193. C3 | #5157 | 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×D24 | 2 |
| #63916 | 2 |
| C3×#818 | 2 |
| #63562 | 2 |
| #5157 | 3 |
| #4883 | 3 |