Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
208 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 208 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. C9×#237 | C2 | semidirect |
| 2. #88642 | C2 | semidirect |
| 3. #88544 | C2 | semidirect |
| 4. C3×#3672 | C2 | semidirect |
| 5. #88427 | C2 | semidirect |
| 6. #88426 | C2 | semidirect |
| 7. D3×C9⋊C8 | C2 | semidirect |
| 34. #3672 | D3 | semidirect |
| 76. #237 | D9 | semidirect |
| 107. C3×C9 | #135 | semidirect |
| 170. C9 | #916 | semidirect |
| 201. C3 | #63513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#237 | 2 |
| #88642 | 2 |
| #88544 | 2 |
| C3×#3672 | 2 |
| #88427 | 2 |
| #88426 | 2 |
| D3×C9⋊C8 | 2 |
| #63935 | 3 |
| #63513 | 3 |