Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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. #79337 | C2 | semidirect |
| 3. #70828 | C2 | semidirect |
| 4. #70817 | C2 | semidirect |
| 5. #70808 | C2 | semidirect |
| 6. C3×#1308 | C2 | semidirect |
| 7. #67757 | C2 | semidirect |
| 33. #1308 | D3 | semidirect |
| 324. C3 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79349 | 2 |
| #79337 | 2 |
| #70828 | 2 |
| #70817 | 2 |
| #70808 | 2 |
| C3×#1308 | 2 |
| #67757 | 2 |
| #9333 | 3 |