Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1164 conjugacy classes of subgroups.
The subgroup lattice has 405 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589422 | C2 | direct (N × H) |
| 11. C2×C32×M16 | C4 | semidirect |
| 13. C22×C32×C8 | C4 | semidirect |
| 24. C2×#3748 | C4 | semidirect |
| 25. C2×#3748 | C4 | semidirect |
| 54. C2×C32×C8 | C2×C4 | semidirect |
| 64. #3748 | C2×C4 | semidirect |
| 74. C2×C3×M16 | Dic3 | semidirect |
| 76. C22×C3×C8 | Dic3 | semidirect |
| 157. C2×C3×C8 | C2×Dic3 | semidirect |
| 205. C2×M16 | C3⋊Dic3 | semidirect |
| 208. C22×C8 | C3⋊Dic3 | semidirect |
| 262. C2×C32 | #344 | semidirect |
| 293. C2×C8 | C2×C3⋊Dic3 | semidirect |
| 323. C32 | C2×#344 | semidirect |
| 370. C2×C3 | #4556 | semidirect |
| 395. C3 | C2×#4556 | semidirect |
| 402. C2 | #10589422 | direct (N × H) |
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 |
| #10589422 | 2 |
| C2×#4556 | 3 |