Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
468 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 468 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. #79338 | C2 | semidirect |
| 3. #70827 | C2 | semidirect |
| 4. #70504 | C2 | semidirect |
| 5. #70496 | C2 | semidirect |
| 6. C3×#1307 | C2 | semidirect |
| 7. #67757 | C2 | semidirect |
| 35. #1307 | D3 | semidirect |
| 352. C3 | #9529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79343 | 2 |
| #79338 | 2 |
| #70827 | 2 |
| #70504 | 2 |
| #70496 | 2 |
| C3×#1307 | 2 |
| #67757 | 2 |
| #9529 | 3 |