Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #79329 | C2 | semidirect |
| 3. #70832 | C2 | semidirect |
| 4. #69866 | C2 | semidirect |
| 5. #69859 | C2 | semidirect |
| 6. C3×#1291 | C2 | semidirect |
| 7. #67748 | C2 | semidirect |
| 17. #4851 | C4 | semidirect |
| 18. #4848 | C4 | semidirect |
| 19. #4846 | C4 | semidirect |
| 20. #4843 | C4 | semidirect |
| 40. #1291 | D3 | semidirect |
| 398. C3 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79347 | 2 |
| #79329 | 2 |
| #70832 | 2 |
| #69866 | 2 |
| #69859 | 2 |
| C3×#1291 | 2 |
| #67748 | 2 |
| #9162 | 3 |