Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1770 conjugacy classes of subgroups.
The subgroup lattice has 286 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #78546 | C2 | semidirect |
| 6. #78545 | C2 | semidirect |
| 7. #78479 | C2 | semidirect |
| 8. #78442 | C2 | semidirect |
| 31. #4702 | C22 | semidirect |
| 32. #4683 | C22 | semidirect |
| 33. #4683 | C22 | semidirect |
| 34. #4682 | C22 | semidirect |
| 35. #4680 | C22 | semidirect |
| 45. C2×C3×M16 | Q8 | semidirect |
| 47. C22×C3×C8 | Q8 | semidirect |
| 140. C2×M16 | Dic6 | semidirect |
| 142. C22×C8 | Dic6 | semidirect |
| 280. C3 | #60660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85725 | 2 |
| C2×C3×#405 | 2 |
| #83752 | 2 |
| C2×#5106 | 2 |
| #78546 | 2 |
| #78545 | 2 |
| #78479 | 2 |
| #78442 | 2 |
| #60660 | 3 |