Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1129 conjugacy classes of subgroups.
The subgroup lattice has 264 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3×#819 | C2 | direct (N × H) |
| 5. C22×#819 | C3 | direct (N × H) |
| 13. C3×#819 | C22 | direct (N × H) |
| 20. C2×#819 | C2×C3 | direct (N × H) |
| 54. #819 | C22×C3 | direct (N × H) |
| 111. C22×C32 | #108 | semidirect |
| 173. C2×C32 | C2×#108 | semidirect |
| 198. C22×C3 | #819 | direct (N × H) |
| 199. C22×C3 | C3×#108 | semidirect |
| 218. C32 | C22×#108 | semidirect |
| 242. C2×C3 | C2×#819 | direct (N × H) |
| 243. C2×C3 | C2×C3×#108 | semidirect |
| 248. C22 | C3×#819 | direct (N × H) |
| 257. C3 | C22×#819 | direct (N × H) |
| 258. C3 | C22×C3×#108 | semidirect |
| 261. C2 | C2×C3×#819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C8 | 2 |
| C22×C3×#208 | 2 |
| C2×C3×#819 | 2 |
| C22×C3×#108 | 3 |
| C22×#819 | 3 |