Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 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. C3×#1568 | C2 | semidirect |
| 3. #70836 | C2 | semidirect |
| 5. #70813 | C2 | semidirect |
| 7. #69751 | C2 | semidirect |
| 18. #4694 | C4 | semidirect |
| 19. #4693 | C4 | semidirect |
| 22. #4681 | C4 | semidirect |
| 23. #4680 | C4 | semidirect |
| 34. #1568 | D3 | semidirect |
| 347. C3 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78468 | 2 |
| C3×#1568 | 2 |
| #70836 | 2 |
| #70832 | 2 |
| #70813 | 2 |
| #70806 | 2 |
| #69751 | 2 |
| #9766 | 3 |