Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
476 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 255 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×C3×Q8×C9 | C2 | semidirect |
| 2. C9×#239 | C2 | semidirect |
| 3. D3×Q8×C9 | C2 | semidirect |
| 4. C9×#235 | C2 | semidirect |
| 21. C2×Q8×C9 | D3 | semidirect |
| 27. #1007 | C9 | direct (N × H) |
| 49. C2×C3×Q8 | C2×C9 | semidirect |
| 51. #239 | C2×C9 | semidirect |
| 52. D3×Q8 | C2×C9 | semidirect |
| 53. #235 | C2×C9 | semidirect |
| 65. C3×C9 | 2−1+4 | semidirect |
| 91. C2×Q8 | D3×C9 | semidirect |
| 104. C9 | #1007 | direct (N × H) |
| 124. C3 | C9×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C9×#239 | 2 |
| D3×Q8×C9 | 2 |
| C9×#235 | 2 |
| C3×#1007 | 3 |
| C9×2−1+4 | 3 |