Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1536 conjugacy classes of subgroups.
The subgroup lattice has 210 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10592698 | C2 | direct (N × H) |
| 5. C2×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 19. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 139. C2×C32 | #424 | semidirect |
| 171. C32 | C2×#424 | semidirect |
| 190. C2×C3 | #4999 | semidirect |
| 204. C3 | C2×#4999 | semidirect |
| 206. C2 | #10592698 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#117 | 2 |
| C22×#3748 | 2 |
| C23×C3⋊(C3⋊C8) | 2 |
| #10592698 | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| C2×#4999 | 3 |