Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1117 conjugacy classes of subgroups.
The subgroup lattice has 351 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #69416 | C3 | direct (N × H) |
| 9. C32×#95 | C4 | semidirect |
| 48. C3×#95 | Dic3 | semidirect |
| 49. C3×#95 | C3×C4 | semidirect |
| 144. #95 | C3×Dic3 | semidirect |
| 278. C32 | #1443 | semidirect |
| 341. C3 | #69416 | direct (N × H) |
| 342. C3 | C3×#1443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#95 | 2 |
| C2×C3×C3⋊#95 | 2 |
| C3×#1443 | 3 |
| #69416 | 3 |