Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1801 conjugacy classes of subgroups.
The subgroup lattice has 302 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#63565 | C2 | direct (N × H) |
| 12. C22×C3×Dic6 | C4 | semidirect |
| 18. #63565 | C22 | direct (N × H) |
| 40. C2×C3×Dic6 | C2×C4 | semidirect |
| 60. C22×Dic6 | Dic3 | semidirect |
| 89. C3×Dic6 | C22×C4 | semidirect |
| 126. C2×Dic6 | C2×Dic3 | semidirect |
| 138. C22×C32 | #103 | semidirect |
| 200. Dic6 | C22×Dic3 | semidirect |
| 204. C2×C32 | C2×#103 | semidirect |
| 231. C22×C3 | #810 | semidirect |
| 232. C22×C3 | #835 | semidirect |
| 254. C32 | C22×#103 | semidirect |
| 276. C2×C3 | C2×#810 | semidirect |
| 277. C2×C3 | C2×#835 | semidirect |
| 284. C22 | #63565 | direct (N × H) |
| 295. C3 | C22×#810 | semidirect |
| 296. C3 | C22×#835 | semidirect |
| 297. C2 | C2×#63565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Dic6 | 2 |
| C23×C3⋊(C3⋊C8) | 2 |
| C22×C3×C4⋊Dic3 | 2 |
| C2×#63565 | 2 |
| C22×#835 | 3 |
| C22×#810 | 3 |