Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. C3×#2981 | C2 | semidirect |
| 3. #71812 | C2 | semidirect |
| 4. #70832 | C2 | semidirect |
| 5. #70765 | C2 | semidirect |
| 6. #67757 | C2 | semidirect |
| 7. #67737 | C2 | semidirect |
| 17. #5093 | C4 | semidirect |
| 18. #5088 | C4 | semidirect |
| 19. #5076 | C4 | semidirect |
| 20. #5073 | C4 | semidirect |
| 31. #2981 | 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 |
|---|---|
| C3×#2981 | 2 |
| #83304 | 2 |
| #71812 | 2 |
| #70832 | 2 |
| #70765 | 2 |
| #67757 | 2 |
| #67737 | 2 |
| #9281 | 3 |