Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4121 conjugacy classes of subgroups; only the 1290 normal subgroups are shown.
This group has 4121 conjugacy classes of subgroups — too many to draw. Only its 1290 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. C23×C3×D12 | C2 | semidirect |
| 2. C23×C32×C8 | C2 | semidirect |
| 3. C22×C3×D24 | C2 | direct (N × H) |
| 5. C23×D24 | C3 | direct (N × H) |
| 9. C22×C3×D12 | C22 | semidirect |
| 10. C22×C32×C8 | C22 | semidirect |
| 11. C2×C3×D24 | C22 | direct (N × H) |
| 13. C23×D12 | C2×C3 | semidirect |
| 16. C23×C3×C8 | D3 | semidirect |
| 17. C23×C3×C8 | C2×C3 | semidirect |
| 18. C22×D24 | C2×C3 | direct (N × H) |
| 25. C2×C3×D12 | C23 | semidirect |
| 26. C2×C32×C8 | C23 | semidirect |
| 27. C3×D24 | C23 | direct (N × H) |
| 37. C22×D12 | C22×C3 | semidirect |
| 40. C22×C3×C8 | C2×D3 | semidirect |
| 41. C22×C3×C8 | C22×C3 | semidirect |
| 42. C2×D24 | C22×C3 | direct (N × H) |
| 43. C23×C32 | D8 | semidirect |
| 50. C3×D12 | C24 | semidirect |
| 51. C32×C8 | C24 | semidirect |
| 54. C23×C8 | C3×D3 | semidirect |
| 71. C2×D12 | C23×C3 | semidirect |
| 74. C2×C3×C8 | C22×D3 | semidirect |
| 75. C2×C3×C8 | C23×C3 | semidirect |
| 76. D24 | C23×C3 | direct (N × H) |
| 77. C22×C32 | C2×D8 | semidirect |
| 88. C22×C8 | C2×C3×D3 | semidirect |
| 93. C23×C3 | D24 | direct (N × H) |
| 94. C23×C3 | C3×D8 | semidirect |
| 108. D12 | C24×C3 | semidirect |
| 110. C3×C8 | C23×D3 | semidirect |
| 111. C3×C8 | C24×C3 | semidirect |
| 112. C2×C32 | C22×D8 | semidirect |
| 123. C2×C8 | C22×C3×D3 | semidirect |
| 128. C22×C3 | C2×D24 | direct (N × H) |
| 129. C22×C3 | C2×C3×D8 | semidirect |
| 140. C32 | C23×D8 | semidirect |
| 143. C23 | C3×D24 | direct (N × H) |
| 149. C8 | C23×C3×D3 | semidirect |
| 153. C2×C3 | C22×D24 | direct (N × H) |
| 154. C2×C3 | C22×C3×D8 | semidirect |
| 160. C22 | C2×C3×D24 | direct (N × H) |
| 165. C3 | C23×D24 | direct (N × H) |
| 166. C3 | C23×C3×D8 | semidirect |
| 168. C2 | C22×C3×D24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D12 | 2 |
| C23×C32×C8 | 2 |
| C22×C3×D24 | 2 |
| C23×C3×D8 | 3 |
| C23×D24 | 3 |