Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×C3⋊D9 | C2 | semidirect |
| 2. C2×C4×D3×C9 | C2 | semidirect |
| 4. C3×C4×Dic9 | C2 | semidirect |
| 5. (C2×D3)⋊Dic9 | C2 | semidirect |
| 6. #88445 | C2 | semidirect |
| 7. Dic9⋊Dic3 | C2 | semidirect |
| 19. #6195 | C4 | direct (N × H) |
| 34. C4×Dic9 | D3 | semidirect |
| 38. C2×C3⋊D9 | C2×C4 | semidirect |
| 41. C2×D3×C9 | C2×C4 | semidirect |
| 42. C3×C4×C9 | D4 | semidirect |
| 46. C3×Dic9 | C2×C4 | semidirect |
| 84. C2×C4×D3 | D9 | semidirect |
| 118. C4×C9 | D12 | semidirect |
| 122. Dic9 | C4×D3 | semidirect |
| 124. C3×C9 | C4×D4 | semidirect |
| 187. C2×D3 | C4×D9 | semidirect |
| 192. C3×C4 | #611 | semidirect |
| 202. C9 | C4×D12 | semidirect |
| 238. C4 | #6195 | direct (N × H) |
| 240. C3 | C4×#611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D9 | 2 |
| C2×C4×D3×C9 | 2 |
| C2×#6195 | 2 |
| C3×C4×Dic9 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| #88445 | 2 |
| Dic9⋊Dic3 | 2 |
| C4×#626 | 3 |
| C4×#611 | 3 |