Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1296 conjugacy classes of subgroups.
The subgroup lattice has 333 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589420 | C2 | direct (N × H) |
| 10. C2×C32×M16 | C4 | semidirect |
| 21. C2×#3748 | C4 | semidirect |
| 45. C32×M16 | C2×C4 | semidirect |
| 54. #3748 | C2×C4 | semidirect |
| 62. C2×C3×M16 | Dic3 | semidirect |
| 128. C3×M16 | C2×Dic3 | semidirect |
| 168. C2×M16 | C3⋊Dic3 | semidirect |
| 212. C2×C32 | #343 | semidirect |
| 236. M16 | C2×C3⋊Dic3 | semidirect |
| 265. C32 | C2×#343 | semidirect |
| 300. C2×C3 | #4554 | semidirect |
| 324. C3 | C2×#4554 | semidirect |
| 328. C2 | #10589420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×M16 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C22×#3748 | 2 |
| #10589420 | 2 |
| C2×#4554 | 3 |