Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2040 conjugacy classes of subgroups.
The subgroup lattice has 447 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589393 | C2 | direct (N × H) |
| 9. C23×C3⋊Dic3 | C4 | semidirect |
| 12. C2×C32×C22⋊C4 | C4 | semidirect |
| 20. C2×#3757 | C4 | semidirect |
| 21. C2×#3757 | C4 | semidirect |
| 49. C22×C3⋊Dic3 | C2×C4 | semidirect |
| 52. C32×C22⋊C4 | C2×C4 | semidirect |
| 59. #3757 | C2×C4 | semidirect |
| 67. C2×C3×C22⋊C4 | Dic3 | semidirect |
| 151. C3×C22⋊C4 | C2×Dic3 | semidirect |
| 212. C2×C22⋊C4 | C3⋊Dic3 | semidirect |
| 267. C2×C32 | #342 | semidirect |
| 301. C22⋊C4 | C2×C3⋊Dic3 | semidirect |
| 339. C32 | C2×#342 | semidirect |
| 393. C2×C3 | #4527 | semidirect |
| 433. C3 | C2×#4527 | semidirect |
| 443. C2 | #10589393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C22⋊C4 | 2 |
| C22×#3757 | 2 |
| #10589393 | 2 |
| C2×#4527 | 3 |