Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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. #79314 | C2 | semidirect |
| 3. #70830 | C2 | semidirect |
| 6. C3×#1285 | C2 | semidirect |
| 7. #67621 | C2 | semidirect |
| 36. #1285 | D3 | semidirect |
| 376. C3 | #9458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79314 | 2 |
| #73712 | 2 |
| #70830 | 2 |
| #70818 | 2 |
| C3×#1285 | 2 |
| #67621 | 2 |
| #9458 | 3 |