Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1653 conjugacy classes of subgroups.
The subgroup lattice has 404 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10591099 | C2 | direct (N × H) |
| 5. C2×#63565 | C2 | semidirect |
| 13. C22×C3×Dic6 | C4 | semidirect |
| 24. #63565 | C22 | semidirect |
| 54. C2×C3×Dic6 | C2×C4 | semidirect |
| 78. C22×Dic6 | Dic3 | semidirect |
| 175. C2×Dic6 | C2×Dic3 | semidirect |
| 284. C2×C32 | #419 | semidirect |
| 348. C32 | C2×#419 | semidirect |
| 378. C2×C3 | #5004 | semidirect |
| 379. C2×C3 | #5225 | semidirect |
| 397. C3 | C2×#5004 | semidirect |
| 398. C3 | C2×#5225 | semidirect |
| 400. C2 | #10591099 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Dic6 | 2 |
| C22×#3748 | 2 |
| C2×C3×#926 | 2 |
| #10591099 | 2 |
| C2×#63565 | 2 |
| C2×#5225 | 3 |
| C2×#5004 | 3 |