Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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×C9×D12 | C2 | semidirect |
| 2. C3×#3697 | C2 | semidirect |
| 3. #88532 | C2 | semidirect |
| 4. #88423 | C2 | semidirect |
| 5. #88421 | C2 | semidirect |
| 13. C3×D36 | C22 | semidirect |
| 15. C3×Dic18 | C22 | semidirect |
| 16. C3⋊(C9⋊C8) | C22 | semidirect |
| 23. #3697 | D3 | semidirect |
| 52. D36 | C2×D3 | semidirect |
| 54. Dic18 | C2×D3 | semidirect |
| 64. C2×D12 | D9 | semidirect |
| 90. C3×C9 | AGL(1,ℤ/8) | semidirect |
| 145. C9 | #949 | semidirect |
| 173. C3 | #63495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C3×#3697 | 2 |
| #88532 | 2 |
| #88423 | 2 |
| #88421 | 2 |
| #63823 | 3 |
| #63495 | 3 |