Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3537 conjugacy classes of subgroups.
The subgroup lattice has 294 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×Dic3×Dic6 | C2 | direct (N × H) |
| 14. C22×C3×Dic6 | C4 | semidirect |
| 20. Dic3×Dic6 | C22 | direct (N × H) |
| 41. C22×C3×Dic3 | Q8 | semidirect |
| 45. C2×C3×Dic6 | C2×C4 | semidirect |
| 66. C22×Dic6 | Dic3 | direct (N × H) |
| 89. C2×C3×Dic3 | C2×Q8 | semidirect |
| 93. C3×Dic6 | C22×C4 | semidirect |
| 124. C22×Dic3 | Dic6 | direct (N × H) |
| 129. C2×Dic6 | C2×Dic3 | direct (N × H) |
| 140. C22×C32 | C4×Q8 | semidirect |
| 149. C3×Dic3 | C22×Q8 | semidirect |
| 194. C2×Dic3 | C2×Dic6 | direct (N × H) |
| 199. Dic6 | C22×Dic3 | direct (N × H) |
| 200. C2×C32 | C2×C4×Q8 | semidirect |
| 226. C22×C3 | C4×Dic6 | semidirect |
| 227. C22×C3 | Q8×Dic3 | semidirect |
| 246. Dic3 | C22×Dic6 | direct (N × H) |
| 248. C32 | C22×C4×Q8 | semidirect |
| 268. C2×C3 | C2×C4×Dic6 | semidirect |
| 269. C2×C3 | C2×Q8×Dic3 | semidirect |
| 276. C22 | Dic3×Dic6 | direct (N × H) |
| 287. C3 | C22×C4×Dic6 | semidirect |
| 288. C3 | C22×Q8×Dic3 | semidirect |
| 289. C2 | C2×Dic3×Dic6 | 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 |
| C22×C3×C4×Dic3 | 2 |
| C22×Dic3⋊Dic3 | 2 |
| C22×Dic32 | 2 |
| C2×Dic3×Dic6 | 2 |
| C22×Q8×Dic3 | 3 |
| C22×C4×Dic6 | 3 |