Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1193 conjugacy classes of subgroups.
The subgroup lattice has 303 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10589163 | C2 | direct (N × H) |
| 8. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 12. C2×C3×C4⋊Dic3 | C4 | semidirect |
| 32. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 35. C3×C4⋊Dic3 | C2×C4 | semidirect |
| 47. C2×C4⋊Dic3 | Dic3 | semidirect |
| 108. C4⋊Dic3 | C2×Dic3 | semidirect |
| 186. C2×C32 | #340 | semidirect |
| 244. C32 | C2×#340 | semidirect |
| 271. C2×C3 | #4529 | semidirect |
| 295. C3 | C2×#4529 | semidirect |
| 296. C2 | #10589163 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C3⋊C8) | 2 |
| C22×C3×C4⋊Dic3 | 2 |
| #10589163 | 2 |
| C2×#4529 | 3 |