Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 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. C33×M16 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 5. C3×#825 | C3 | direct (N × H) |
| 9. C32×D12 | C4 | semidirect |
| 11. C32×Dic6 | C4 | semidirect |
| 16. C32×M16 | D3 | semidirect |
| 17. C32×M16 | C2×C3 | semidirect |
| 19. C3×C4×Dic3 | C2×C3 | semidirect |
| 27. #825 | C32 | direct (N × H) |
| 38. C3×D12 | C3×C4 | semidirect |
| 40. C3×Dic6 | C3×C4 | semidirect |
| 50. C3×M16 | C3×D3 | semidirect |
| 51. C3×M16 | C2×C32 | semidirect |
| 53. C4×Dic3 | C2×C32 | semidirect |
| 70. C33 | #104 | semidirect |
| 81. D12 | C32×C4 | semidirect |
| 83. Dic6 | C32×C4 | semidirect |
| 96. M16 | C32×D3 | semidirect |
| 114. C32 | #825 | direct (N × H) |
| 115. C32 | C3×#104 | semidirect |
| 138. C3 | C3×#825 | direct (N × H) |
| 139. C3 | C32×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#235 | 2 |
| C33×M16 | 2 |
| C32×C4×Dic3 | 2 |
| C32×#104 | 3 |
| C3×#825 | 3 |