Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
308 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 67 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×C9×D12 | C2 | semidirect |
| 2. C2×#6194 | C2 | semidirect |
| 3. C2×#6194 | C2 | semidirect |
| 4. C2×D3×Dic9 | C2 | semidirect |
| 5. #88534 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 7. (C2×D3)⋊Dic9 | C2 | semidirect |
| 33. (C2×D9)⋊C4 | D3 | semidirect |
| 42. C2×D3×C9 | D4 | semidirect |
| 48. C3⋊Dic9 | D4 | semidirect |
| 89. C2×D12 | D9 | semidirect |
| 131. C3×C9 | #121 | semidirect |
| 199. C2×D3 | #611 | semidirect |
| 213. C9 | #884 | semidirect |
| 255. C3 | #63501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C2×#6194 | 2 |
| C2×D3×Dic9 | 2 |
| #88534 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| #63885 | 3 |
| #63501 | 3 |