Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 2. #88855 | C2 | semidirect |
| 3. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 9. C32×D12 | C4 | semidirect |
| 11. C32×Dic6 | C4 | semidirect |
| 15. C4×C3⋊Dic3 | D3 | semidirect |
| 38. C3×D12 | Dic3 | semidirect |
| 40. C3×Dic6 | Dic3 | semidirect |
| 70. C33 | #104 | semidirect |
| 81. D12 | C3⋊Dic3 | semidirect |
| 83. Dic6 | C3⋊Dic3 | semidirect |
| 114. C32 | #805 | semidirect |
| 115. C32 | #837 | semidirect |
| 138. C3 | #63569 | semidirect |
| 139. C3 | #63664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#235 | 2 |
| #88855 | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| #63664 | 3 |
| #63569 | 3 |