Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #83280 | C2 | semidirect |
| 3. C3×#1530 | C2 | semidirect |
| 4. #70801 | C2 | semidirect |
| 5. #69798 | C2 | semidirect |
| 6. #67757 | C2 | semidirect |
| 7. #67660 | C2 | semidirect |
| 33. #1530 | D3 | semidirect |
| 344. C3 | #9283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83303 | 2 |
| #83280 | 2 |
| C3×#1530 | 2 |
| #70801 | 2 |
| #69798 | 2 |
| #67757 | 2 |
| #67660 | 2 |
| #9283 | 3 |