Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1045 conjugacy classes of subgroups.
The subgroup lattice has 437 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589163 | C2 | semidirect |
| 11. C2×#3748 | C4 | semidirect |
| 15. C3×#926 | C4 | semidirect |
| 18. C2×C3×C4⋊Dic3 | C4 | semidirect |
| 47. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 53. C3×C4⋊Dic3 | C2×C4 | semidirect |
| 72. #926 | Dic3 | semidirect |
| 75. C2×C4⋊Dic3 | Dic3 | semidirect |
| 168. C4⋊Dic3 | C2×Dic3 | semidirect |
| 365. C32 | #1736 | semidirect |
| 428. C3 | #71558 | semidirect |
| 429. C3 | #71581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3748 | 2 |
| C2×C3×#926 | 2 |
| C22×C3×C4⋊Dic3 | 2 |
| #10589163 | 2 |
| #71581 | 3 |
| #71558 | 3 |