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. #78512 | C2 | semidirect |
| 3. C3×#1525 | C2 | semidirect |
| 4. #71812 | C2 | semidirect |
| 5. #69866 | C2 | semidirect |
| 6. #67670 | C2 | semidirect |
| 7. #67665 | C2 | semidirect |
| 15. #5094 | C4 | semidirect |
| 16. #5087 | C4 | semidirect |
| 17. #5075 | C4 | semidirect |
| 18. #5072 | C4 | semidirect |
| 37. #1525 | 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 |
|---|---|
| #83301 | 2 |
| #78512 | 2 |
| C3×#1525 | 2 |
| #71812 | 2 |
| #69866 | 2 |
| #67670 | 2 |
| #67665 | 2 |
| #9162 | 3 |