Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1841 conjugacy classes of subgroups.
The subgroup lattice has 307 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×#63566 | C2 | direct (N × H) |
| 12. C22×C3×Dic6 | C4 | semidirect |
| 18. #63566 | C22 | direct (N × H) |
| 40. C2×C3×Dic6 | C2×C4 | semidirect |
| 61. C22×Dic6 | Dic3 | semidirect |
| 90. C3×Dic6 | C22×C4 | semidirect |
| 129. C2×Dic6 | C2×Dic3 | semidirect |
| 141. C22×C32 | #103 | semidirect |
| 205. Dic6 | C22×Dic3 | semidirect |
| 208. C2×C32 | C2×#103 | semidirect |
| 235. C22×C3 | #816 | semidirect |
| 236. C22×C3 | #835 | semidirect |
| 259. C32 | C22×#103 | semidirect |
| 281. C2×C3 | C2×#816 | semidirect |
| 282. C2×C3 | C2×#835 | semidirect |
| 289. C22 | #63566 | direct (N × H) |
| 300. C3 | C22×#816 | semidirect |
| 301. C3 | C22×#835 | semidirect |
| 302. C2 | C2×#63566 | 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 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C23×C3×C3⋊C8 | 2 |
| C2×#63566 | 2 |
| C22×#835 | 3 |
| C22×#816 | 3 |