Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
576 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 144 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. C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. #88807 | C2 | semidirect |
| 12. C3×C4×C3⋊D3 | C4 | semidirect |
| 22. C3×C4×Dic3 | D3 | semidirect |
| 44. C4×C3⋊D3 | Dic3 | semidirect |
| 61. C4×Dic3 | C3⋊D3 | semidirect |
| 80. C33 | #117 | semidirect |
| 126. C32 | #872 | semidirect |
| 127. C32 | #926 | semidirect |
| 150. C3 | #63855 | semidirect |
| 151. C3 | #64081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C3⋊D3 | 2 |
| C4×C3⋊(C3⋊Dic3) | 2 |
| C32×C4×Dic3 | 2 |
| #88807 | 2 |
| #88803 | 2 |
| #64081 | 3 |
| #63855 | 3 |