Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2494 conjugacy classes of subgroups.
The subgroup lattice has 272 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#4530 | C2 | direct (N × H) |
| 13. C22×#208 | C4 | semidirect |
| 16. #4530 | C22 | direct (N × H) |
| 41. C2×#208 | C2×C4 | semidirect |
| 89. #208 | C22×C4 | semidirect |
| 192. C22×C3 | #343 | semidirect |
| 240. C2×C3 | C2×#343 | semidirect |
| 251. C22 | #4530 | direct (N × H) |
| 263. C3 | C22×#343 | semidirect |
| 267. C2 | C2×#4530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4⋊C4 | 2 |
| C23×#208 | 2 |
| C2×#4530 | 2 |
| C22×#343 | 3 |