Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 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 |
|---|---|---|
| 2. #74265 | C2 | semidirect |
| 5. #70824 | C2 | semidirect |
| 6. #67752 | C2 | semidirect |
| 7. #67633 | C2 | semidirect |
| 14. #5092 | C4 | semidirect |
| 15. #5076 | C4 | semidirect |
| 307. C3 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83288 | 2 |
| #74265 | 2 |
| C3×#1514 | 2 |
| #71813 | 2 |
| #70824 | 2 |
| #67752 | 2 |
| #67633 | 2 |
| #9429 | 3 |