Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #70836 | C2 | semidirect |
| 5. #69862 | C2 | semidirect |
| 6. C3×#1291 | C2 | semidirect |
| 7. #67748 | C2 | semidirect |
| 17. #4850 | C4 | semidirect |
| 18. #4849 | C4 | semidirect |
| 19. #4842 | C4 | semidirect |
| 20. #4841 | C4 | semidirect |
| 40. #1291 | D3 | semidirect |
| 383. C3 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79348 | 2 |
| #79329 | 2 |
| #70836 | 2 |
| #69866 | 2 |
| #69862 | 2 |
| C3×#1291 | 2 |
| #67748 | 2 |
| #9160 | 3 |