Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 442 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. C3×#1536 | C2 | semidirect |
| 4. #71800 | C2 | semidirect |
| 5. #70816 | C2 | semidirect |
| 6. #67757 | C2 | semidirect |
| 7. #67755 | C2 | semidirect |
| 33. #1536 | D3 | semidirect |
| 340. C3 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83308 | 2 |
| #79338 | 2 |
| C3×#1536 | 2 |
| #71800 | 2 |
| #70816 | 2 |
| #67757 | 2 |
| #67755 | 2 |
| #9371 | 3 |