Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1032 conjugacy classes of subgroups.
The subgroup lattice has 285 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#63662 | C2 | semidirect |
| 4. C4×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C2×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 10. C32×#124 | C4 | semidirect |
| 54. C3×#124 | Dic3 | semidirect |
| 142. #124 | C3⋊Dic3 | semidirect |
| 226. C32 | #1983 | semidirect |
| 277. C3 | #71721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#124 | 2 |
| C2×#63662 | 2 |
| C2×#63659 | 2 |
| C4×C4⋊(C3⋊Dic3) | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #71721 | 3 |