Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #70824 | C2 | semidirect |
| 5. #70460 | C2 | semidirect |
| 6. #67750 | C2 | semidirect |
| 7. #67708 | C2 | semidirect |
| 19. #5064 | C4 | semidirect |
| 20. #5055 | C4 | semidirect |
| 370. C3 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2992 | 2 |
| #83123 | 2 |
| #71755 | 2 |
| #70824 | 2 |
| #70460 | 2 |
| #67750 | 2 |
| #67708 | 2 |
| #9375 | 3 |