Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1344 conjugacy classes of subgroups.
The subgroup lattice has 282 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589417 | C2 | semidirect |
| 10. C2×C32×M16 | C4 | semidirect |
| 14. #64135 | C4 | semidirect |
| 17. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 41. C2×C32×C8 | C2×C4 | semidirect |
| 47. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 54. C2×C3×M16 | Dic3 | semidirect |
| 111. C2×C3×C8 | C2×Dic3 | semidirect |
| 140. C2×M16 | C3⋊Dic3 | semidirect |
| 199. C2×C8 | C2×C3⋊Dic3 | semidirect |
| 224. C32 | #1736 | semidirect |
| 274. C3 | #71985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×M16 | 2 |
| C2×#64135 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| #10589417 | 2 |
| #71985 | 3 |