Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2400 conjugacy classes of subgroups.
The subgroup lattice has 306 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #10592627 | C2 | direct (N × H) |
| 16. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 51. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 82. C2×C32×C4 | C4⋊C4 | semidirect |
| 143. C32×C4 | C2×C4⋊C4 | semidirect |
| 174. C2×C3×C4 | Dic3⋊C4 | semidirect |
| 188. C2×C32 | #389 | semidirect |
| 237. C3×C4 | C2×Dic3⋊C4 | semidirect |
| 240. C32 | C2×#389 | semidirect |
| 263. C2×C4 | #3750 | semidirect |
| 269. C2×C3 | #4928 | semidirect |
| 295. C4 | C2×#3750 | semidirect |
| 296. C3 | C2×#4928 | semidirect |
| 297. C2 | #10592627 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C42 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C22×#3750 | 2 |
| C2×#63658 | 2 |
| #10592627 | 2 |
| C2×#4928 | 3 |