Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
934 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×A4×D12 | C2 | semidirect |
| 2. C2×C3×C8×A4 | C2 | semidirect |
| 3. A4×D24 | C2 | direct (N × H) |
| 4. C23×D24 | C3 | semidirect |
| 9. A4×D12 | C22 | semidirect |
| 11. C3×C8×A4 | C22 | semidirect |
| 12. C23×D12 | C2×C3 | semidirect |
| 14. C23×C3×C8 | C2×C3 | semidirect |
| 19. C22×D24 | C2×C3 | semidirect |
| 22. C2×C8×A4 | D3 | semidirect |
| 41. C22×D12 | C22×C3 | semidirect |
| 50. C22×C3×C8 | C22×C3 | semidirect |
| 60. C2×D24 | A4 | direct (N × H) |
| 62. C8×A4 | C2×D3 | semidirect |
| 64. C2×C3×A4 | D8 | semidirect |
| 77. C23×C8 | C3×D3 | semidirect |
| 110. C2×D12 | C2×A4 | semidirect |
| 123. C2×C3×C8 | C2×A4 | semidirect |
| 127. D24 | C2×A4 | direct (N × H) |
| 131. C3×A4 | C2×D8 | semidirect |
| 156. C22×C8 | C2×C3×D3 | semidirect |
| 161. C23×C3 | C3×D8 | semidirect |
| 180. C2×A4 | D24 | direct (N × H) |
| 202. D12 | C22×A4 | semidirect |
| 206. C3×C8 | C22×A4 | semidirect |
| 247. C2×C8 | D3×A4 | semidirect |
| 259. C22×C3 | C2×C3×D8 | semidirect |
| 272. A4 | C2×D24 | direct (N × H) |
| 299. C23 | C3×D24 | semidirect |
| 319. C8 | C2×D3×A4 | semidirect |
| 328. C2×C3 | A4×D8 | semidirect |
| 349. C22 | C2×C3×D24 | semidirect |
| 357. C3 | C2×A4×D8 | semidirect |
| 363. C2 | A4×D24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×D12 | 2 |
| C2×C3×C8×A4 | 2 |
| A4×D24 | 2 |
| C23×D24 | 3 |
| C2×A4×D8 | 3 |
| C2×C3×D24 | 4 |