Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1452 conjugacy classes of subgroups.
The subgroup lattice has 207 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10592698 | C2 | semidirect |
| 4. #10592623 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 105. C32×C4 | #131 | semidirect |
| 167. C3×C4 | #948 | semidirect |
| 170. C32 | #2906 | semidirect |
| 198. C4 | #64157 | semidirect |
| 201. C3 | #82512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×#41 | 2 |
| C2×#64157 | 2 |
| #10592698 | 2 |
| #10592623 | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #82512 | 3 |