Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
768 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 |
|---|---|---|
| 22. #63643 | C4 | semidirect |
| 253. C32 | #1933 | semidirect |
| 309. C3 | #69767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C8 | 2 |
| C2×#63643 | 2 |
| #10592628 | 2 |
| #10592627 | 2 |
| #10589417 | 2 |
| #69767 | 3 |