Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1173 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10591116 | C2 | direct (N × H) |
| 5. C2×Dic3⋊(C3⋊C8) | C2 | semidirect |
| 20. Dic3⋊(C3⋊C8) | C22 | semidirect |
| 222. C2×C32 | #424 | semidirect |
| 275. C32 | C2×#424 | semidirect |
| 299. C2×C3 | #4999 | semidirect |
| 300. C2×C3 | #5102 | semidirect |
| 317. C3 | C2×#4999 | semidirect |
| 318. C3 | C2×#5102 | semidirect |
| 320. C2 | #10591116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3748 | 2 |
| C2×C3×#926 | 2 |
| C23×C3×C3⋊C8 | 2 |
| #10591116 | 2 |
| C2×Dic3⋊(C3⋊C8) | 2 |
| C2×#5102 | 3 |
| C2×#4999 | 3 |