Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1381 conjugacy classes of subgroups.
The subgroup lattice has 318 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #69419 | C3 | direct (N × H) |
| 11. C32×#95 | C4 | semidirect |
| 49. C3×#95 | Dic3 | semidirect |
| 50. C3×#95 | C3×C4 | semidirect |
| 63. C2×C32×C4 | C4⋊C4 | semidirect |
| 132. #95 | C3×Dic3 | semidirect |
| 175. C2×C3×C4 | C4⋊Dic3 | semidirect |
| 176. C2×C3×C4 | C3×C4⋊C4 | semidirect |
| 250. C32 | #1444 | semidirect |
| 270. C2×C4 | C3×C4⋊Dic3 | semidirect |
| 308. C3 | #69419 | direct (N × H) |
| 309. C3 | C3×#1444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊Dic3 | 2 |
| C2×C32×#95 | 2 |
| C2×C3×C3⋊#95 | 2 |
| C3×#1444 | 3 |
| #69419 | 3 |