Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
480 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 109 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. #73391 | C2 | semidirect |
| 5. #70508 | C2 | semidirect |
| 6. #67713 | C2 | semidirect |
| 7. #67614 | C2 | semidirect |
| 15. #5080 | C4 | semidirect |
| 16. #5070 | C4 | semidirect |
| 356. C3 | #9302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83271 | 2 |
| #73391 | 2 |
| C3×#1963 | 2 |
| #71814 | 2 |
| #70508 | 2 |
| #67713 | 2 |
| #67614 | 2 |
| #9302 | 3 |