Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1193 conjugacy classes of subgroups.
The subgroup lattice has 340 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#4551 | C2 | direct (N × H) |
| 5. C2×#4551 | C3 | direct (N × H) |
| 9. C22×C32×C8 | C4 | semidirect |
| 13. C2×C3×C4⋊Dic3 | C4 | semidirect |
| 21. #4551 | C2×C3 | direct (N × H) |
| 35. C2×C32×C8 | C2×C4 | semidirect |
| 38. C3×C4⋊Dic3 | C2×C4 | semidirect |
| 50. C22×C3×C8 | Dic3 | semidirect |
| 51. C22×C3×C8 | C3×C4 | semidirect |
| 60. C2×C4⋊Dic3 | C3×C4 | semidirect |
| 121. C2×C3×C8 | C2×Dic3 | semidirect |
| 122. C2×C3×C8 | C2×C3×C4 | semidirect |
| 128. C4⋊Dic3 | C2×C3×C4 | semidirect |
| 147. C22×C8 | C3×Dic3 | semidirect |
| 209. C2×C32 | #340 | semidirect |
| 228. C2×C8 | C2×C3×Dic3 | semidirect |
| 276. C32 | C2×#340 | semidirect |
| 303. C2×C3 | #4551 | direct (N × H) |
| 304. C2×C3 | C3×#340 | semidirect |
| 331. C3 | C2×#4551 | direct (N × H) |
| 332. C3 | C2×C3×#340 | semidirect |
| 333. C2 | C3×#4551 | 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×C4⋊Dic3 | 2 |
| C3×#4551 | 2 |
| C2×C3×#340 | 3 |
| C2×#4551 | 3 |