Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
506 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 100 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×C32×D12 | C2 | semidirect |
| 2. C2×C3×#625 | C2 | semidirect |
| 3. C2×C3×#625 | C2 | semidirect |
| 4. C2×C3×D3×Dic3 | C2 | semidirect |
| 5. C3×#3750 | C2 | semidirect |
| 6. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C3×(C2×D3)⋊Dic3 | C2 | semidirect |
| 10. #63885 | C3 | direct (N × H) |
| 29. C2×C3×D12 | D3 | semidirect |
| 30. C2×C3×D12 | C2×C3 | semidirect |
| 32. C2×#625 | C2×C3 | semidirect |
| 33. C2×#625 | C2×C3 | semidirect |
| 34. C2×D3×Dic3 | C2×C3 | semidirect |
| 36. #3750 | C2×C3 | semidirect |
| 40. C3×(C2×D3)⋊C4 | D3 | semidirect |
| 41. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 45. (C2×D3)⋊Dic3 | C2×C3 | semidirect |
| 55. C2×C32×D3 | D4 | semidirect |
| 58. C3×C3⋊Dic3 | D4 | semidirect |
| 124. C2×D12 | C3×D3 | semidirect |
| 133. (C2×D3)⋊C4 | C3×D3 | semidirect |
| 178. C2×C3×D3 | #67 | semidirect |
| 179. C2×C3×D3 | C3×D4 | semidirect |
| 189. C3⋊Dic3 | C3×D4 | semidirect |
| 200. C33 | #121 | semidirect |
| 327. C2×D3 | C3×#67 | semidirect |
| 351. C32 | #884 | semidirect |
| 352. C32 | #939 | semidirect |
| 353. C32 | C3×#121 | semidirect |
| 416. C3 | #63885 | direct (N × H) |
| 417. C3 | C3×#884 | semidirect |
| 418. C3 | C3×#939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D12 | 2 |
| C2×C3×#625 | 2 |
| C2×C3×D3×Dic3 | 2 |
| C3×#3750 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C3×(C2×D3)⋊Dic3 | 2 |
| C3×#939 | 3 |
| C3×#884 | 3 |
| #63885 | 3 |