Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
355 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 178 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. C22×C32×C4 | C2 | semidirect |
| 2. C2×C3×#67 | C2 | semidirect |
| 3. C3×#235 | C2 | direct (N × H) |
| 4. C2×C3×D12 | C2 | semidirect |
| 5. C2×C3×C4×D3 | C2 | semidirect |
| 6. C2×C3×Dic6 | C2 | semidirect |
| 8. C2×#235 | C3 | direct (N × H) |
| 13. C2×C32×C4 | C22 | semidirect |
| 14. C3×#67 | C22 | semidirect |
| 16. C3×D12 | C22 | semidirect |
| 17. C3×C4×D3 | C22 | semidirect |
| 18. C3×Dic6 | C22 | semidirect |
| 25. C22×C3×C4 | D3 | semidirect |
| 26. C22×C3×C4 | C2×C3 | semidirect |
| 27. C2×#67 | C2×C3 | semidirect |
| 28. #235 | C2×C3 | direct (N × H) |
| 29. C2×D12 | C2×C3 | semidirect |
| 30. C2×C4×D3 | C2×C3 | semidirect |
| 31. C2×Dic6 | C2×C3 | semidirect |
| 56. C2×C3×C4 | C2×D3 | semidirect |
| 59. C2×C3×C4 | C22×C3 | semidirect |
| 60. #67 | C22×C3 | semidirect |
| 62. D12 | C22×C3 | semidirect |
| 63. C4×D3 | C22×C3 | semidirect |
| 64. Dic6 | C22×C3 | semidirect |
| 66. C2×C32 | #41 | semidirect |
| 74. C22×C4 | C3×D3 | semidirect |
| 96. C32 | C2×#41 | semidirect |
| 106. C2×C4 | C2×C3×D3 | semidirect |
| 113. C2×C3 | #235 | direct (N × H) |
| 114. C2×C3 | C3×#41 | semidirect |
| 127. C3 | C2×#235 | direct (N × H) |
| 128. C3 | C2×C3×#41 | semidirect |
| 131. C2 | C3×#235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4 | 2 |
| C2×C3×#67 | 2 |
| C3×#235 | 2 |
| C2×C3×D12 | 2 |
| C2×C3×C4×D3 | 2 |
| C2×C3×Dic6 | 2 |
| C2×C3×#41 | 3 |
| C2×#235 | 3 |