Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. #79338 | C2 | semidirect |
| 3. #70832 | C2 | semidirect |
| 4. #70832 | C2 | semidirect |
| 5. #70801 | C2 | semidirect |
| 6. C3×#1287 | C2 | semidirect |
| 7. #67737 | C2 | semidirect |
| 22. #4695 | C4 | semidirect |
| 23. #4694 | C4 | semidirect |
| 24. #4693 | C4 | semidirect |
| 25. #4681 | C4 | semidirect |
| 35. #1287 | D3 | semidirect |
| 350. C3 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79338 | 2 |
| #79304 | 2 |
| #70832 | 2 |
| #70801 | 2 |
| C3×#1287 | 2 |
| #67737 | 2 |
| #9281 | 3 |