Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1669 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10591100 | C2 | direct (N × H) |
| 5. C2×#63566 | C2 | semidirect |
| 13. C22×C3×Dic6 | C4 | semidirect |
| 24. #63566 | C22 | semidirect |
| 54. C2×C3×Dic6 | C2×C4 | semidirect |
| 78. C22×Dic6 | Dic3 | semidirect |
| 178. C2×Dic6 | C2×Dic3 | semidirect |
| 289. C2×C32 | #419 | semidirect |
| 354. C32 | C2×#419 | semidirect |
| 384. C2×C3 | #5120 | semidirect |
| 385. C2×C3 | #5225 | semidirect |
| 403. C3 | C2×#5120 | semidirect |
| 404. C3 | C2×#5225 | semidirect |
| 406. C2 | #10591100 | 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 |
| C2×#64135 | 2 |
| C22×C3×#208 | 2 |
| #10591100 | 2 |
| C2×#63566 | 2 |
| C2×#5225 | 3 |
| C2×#5120 | 3 |