Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1464 conjugacy classes of subgroups.
The subgroup lattice has 321 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589421 | C2 | direct (N × H) |
| 10. C2×C32×M16 | C4 | semidirect |
| 16. #64135 | C4 | semidirect |
| 18. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 22. C2×C4×C3⋊Dic3 | C4 | semidirect |
| 45. C32×M16 | C2×C4 | semidirect |
| 51. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 56. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 62. C2×C3×M16 | Dic3 | semidirect |
| 127. C3×M16 | C2×Dic3 | semidirect |
| 161. C2×M16 | C3⋊Dic3 | semidirect |
| 208. C2×C32 | #339 | semidirect |
| 228. M16 | C2×C3⋊Dic3 | semidirect |
| 258. C32 | C2×#339 | semidirect |
| 292. C2×C3 | #4555 | semidirect |
| 313. C3 | C2×#4555 | semidirect |
| 317. C2 | #10589421 | 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×C4×C3⋊Dic3 | 2 |
| #10589421 | 2 |
| C2×#4555 | 3 |