Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 4. #70815 | C2 | semidirect |
| 5. #70768 | C2 | semidirect |
| 6. C3×#1287 | C2 | semidirect |
| 7. #67755 | C2 | semidirect |
| 36. #1287 | D3 | semidirect |
| 321. C3 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79352 | 2 |
| #79290 | 2 |
| #70816 | 2 |
| #70815 | 2 |
| #70768 | 2 |
| C3×#1287 | 2 |
| #67755 | 2 |
| #9373 | 3 |