Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
204 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 53 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. #88641 | C2 | semidirect |
| 2. #88521 | C2 | semidirect |
| 3. D3×C8×C9 | C2 | semidirect |
| 4. C3×D72 | C2 | semidirect |
| 5. #88415 | C2 | semidirect |
| 22. D72 | D3 | semidirect |
| 62. D3×C8 | D9 | semidirect |
| 76. C3×C9 | #135 | semidirect |
| 119. C9 | #912 | semidirect |
| 140. C3 | #63467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88641 | 2 |
| #88521 | 2 |
| D3×C8×C9 | 2 |
| C3×D72 | 2 |
| #88415 | 2 |
| #63807 | 3 |
| #63467 | 3 |