Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
146 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×#235 | C2 | semidirect |
| 2. C2×C3×D12 | C2 | semidirect |
| 3. C32×M16 | C2 | semidirect |
| 4. C3×D24 | C2 | semidirect |
| 5. C3×#204 | C2 | semidirect |
| 7. #908 | C3 | direct (N × H) |
| 13. C3×D12 | C22 | semidirect |
| 15. C3×Dic6 | C22 | semidirect |
| 16. C32×C8 | C22 | semidirect |
| 19. #235 | C2×C3 | semidirect |
| 20. C2×D12 | C2×C3 | semidirect |
| 24. C3×M16 | D3 | semidirect |
| 25. C3×M16 | C2×C3 | semidirect |
| 26. D24 | C2×C3 | semidirect |
| 27. #204 | C2×C3 | semidirect |
| 50. D12 | C22×C3 | semidirect |
| 52. Dic6 | C22×C3 | semidirect |
| 54. C3×C8 | C2×D3 | semidirect |
| 55. C3×C8 | C22×C3 | semidirect |
| 64. M16 | C3×D3 | semidirect |
| 82. C32 | AGL(1,ℤ/8) | semidirect |
| 91. C8 | C2×C3×D3 | semidirect |
| 110. C3 | #908 | direct (N × H) |
| 111. C3 | C3×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#235 | 2 |
| C2×C3×D12 | 2 |
| C32×M16 | 2 |
| C3×D24 | 2 |
| C3×#204 | 2 |
| C3×AGL(1,ℤ/8) | 3 |
| #908 | 3 |