Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
349 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3796 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. #63916 | C2 | semidirect |
| 4. C2×#3715 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. #63562 | C2 | semidirect |
| 31. C2×D24 | D3 | semidirect |
| 38. #816 | D3 | semidirect |
| 52. C3×D12 | D4 | semidirect |
| 54. C3×Dic6 | D4 | semidirect |
| 147. D12 | #67 | semidirect |
| 156. Dic6 | D12 | semidirect |
| 221. C32 | #449 | semidirect |
| 274. C3 | #4810 | semidirect |
| 275. C3 | #5158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3796 | 2 |
| C2×C3×D24 | 2 |
| #63916 | 2 |
| C2×#3715 | 2 |
| #63647 | 2 |
| C3×#816 | 2 |
| #63562 | 2 |
| #5158 | 3 |
| #4810 | 3 |