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. #10589395 | C2 | semidirect |
| 9. C32×#117 | C4 | semidirect |
| 15. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 19. C2×#3748 | C4 | semidirect |
| 39. C32×C4⋊C4 | C2×C4 | semidirect |
| 48. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 53. C3×#117 | Dic3 | semidirect |
| 109. C3×C4⋊C4 | C2×Dic3 | semidirect |
| 143. #117 | C3⋊Dic3 | semidirect |
| 204. C4⋊C4 | C2×C3⋊Dic3 | semidirect |
| 224. C32 | #1736 | semidirect |
| 274. C3 | #71581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#117 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C22×#3748 | 2 |
| #10589395 | 2 |
| #71581 | 3 |