Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70803 | C2 | semidirect |
| 4. #69441 | C2 | semidirect |
| 6. C3×#1300 | C2 | semidirect |
| 7. #67669 | C2 | semidirect |
| 22. #4715 | C4 | semidirect |
| 23. #4714 | C4 | semidirect |
| 25. #4703 | C4 | semidirect |
| 26. #4702 | C4 | semidirect |
| 41. #1300 | D3 | semidirect |
| 391. C3 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79342 | 2 |
| #78539 | 2 |
| #70803 | 2 |
| #69441 | 2 |
| #69431 | 2 |
| C3×#1300 | 2 |
| #67669 | 2 |
| #8998 | 3 |