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. #10589425 | C2 | direct (N × H) |
| 10. C2×C32×M16 | C4 | semidirect |
| 11. C2×C32×M16 | C4 | semidirect |
| 25. C2×#3748 | C4 | semidirect |
| 27. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 51. C32×M16 | C2×C4 | semidirect |
| 67. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 73. C2×C3×M16 | Dic3 | semidirect |
| 74. C2×C3×M16 | Dic3 | semidirect |
| 154. C3×M16 | C2×Dic3 | semidirect |
| 204. C2×M16 | C3⋊Dic3 | semidirect |
| 205. C2×M16 | C3⋊Dic3 | semidirect |
| 262. C2×C32 | #344 | semidirect |
| 287. M16 | C2×C3⋊Dic3 | semidirect |
| 323. C32 | C2×#344 | semidirect |
| 370. C2×C3 | #4559 | semidirect |
| 395. C3 | C2×#4559 | semidirect |
| 402. C2 | #10589425 | 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 |
| #10589425 | 2 |
| C2×#4559 | 3 |