Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1692 conjugacy classes of subgroups.
The subgroup lattice has 273 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10592821 | C2 | semidirect |
| 5. M16×C3⋊Dic3 | C2 | semidirect |
| 6. #10592800 | C2 | semidirect |
| 9. C2×C32×M16 | C4 | semidirect |
| 20. C2×#3748 | C4 | semidirect |
| 24. #63642 | C22 | semidirect |
| 25. C8×C3⋊Dic3 | C22 | semidirect |
| 43. C32×M16 | C2×C4 | semidirect |
| 44. C2×C32×C8 | C2×C4 | semidirect |
| 53. #3748 | C2×C4 | semidirect |
| 54. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 58. C2×C3×M16 | Dic3 | semidirect |
| 114. C3×M16 | C2×Dic3 | semidirect |
| 115. C2×C3×C8 | C2×Dic3 | semidirect |
| 145. C2×M16 | C3⋊Dic3 | semidirect |
| 199. M16 | C2×C3⋊Dic3 | semidirect |
| 202. C2×C8 | C2×C3⋊Dic3 | semidirect |
| 224. C32 | #2873 | semidirect |
| 266. C3 | #83747 | 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×#3748 | 2 |
| #10592821 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10592800 | 2 |
| #83747 | 3 |