Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #82519 | C2 | semidirect |
| 3. C3×#1759 | C2 | semidirect |
| 4. #69859 | C2 | semidirect |
| 5. #69432 | C2 | semidirect |
| 6. #67670 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 15. #5027 | C4 | semidirect |
| 18. #5020 | C4 | semidirect |
| 19. #5015 | C4 | semidirect |
| 23. #5007 | C4 | semidirect |
| 36. #1759 | D3 | semidirect |
| 398. C3 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82531 | 2 |
| #82519 | 2 |
| C3×#1759 | 2 |
| #69859 | 2 |
| #69432 | 2 |
| #67670 | 2 |
| #67615 | 2 |
| #9162 | 3 |