Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 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×D3×C9 | C2 | semidirect |
| 2. C2×C3×C4×D9 | C2 | semidirect |
| 4. C4×C3⋊Dic9 | C2 | semidirect |
| 5. (C2×D3)⋊Dic9 | C2 | semidirect |
| 6. (C2×D9)⋊Dic3 | C2 | semidirect |
| 7. #88442 | C2 | semidirect |
| 19. #6194 | C4 | direct (N × H) |
| 29. C2×C4×D9 | D3 | semidirect |
| 38. C2×D3×C9 | C2×C4 | semidirect |
| 41. C2×C3×D9 | C2×C4 | semidirect |
| 42. C3×C4×C9 | D4 | semidirect |
| 44. C3⋊Dic9 | C2×C4 | semidirect |
| 82. C2×C4×D3 | D9 | semidirect |
| 111. C2×D9 | C4×D3 | semidirect |
| 114. C4×C9 | #67 | semidirect |
| 121. C3×C9 | C4×D4 | semidirect |
| 179. C2×D3 | C4×D9 | semidirect |
| 183. C3×C4 | #611 | semidirect |
| 195. C9 | C4×#67 | semidirect |
| 230. C4 | #6194 | direct (N × H) |
| 232. 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×D3×C9 | 2 |
| C2×C3×C4×D9 | 2 |
| C2×#6194 | 2 |
| C4×C3⋊Dic9 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| #88442 | 2 |
| C4×#625 | 3 |
| C4×#611 | 3 |