Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 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. #79290 | C2 | semidirect |
| 3. #70765 | C2 | semidirect |
| 4. #69432 | C2 | semidirect |
| 5. #69432 | C2 | semidirect |
| 6. C3×#1274 | C2 | semidirect |
| 7. #67747 | C2 | semidirect |
| 20. #4695 | C4 | semidirect |
| 21. #4694 | C4 | semidirect |
| 22. #4693 | C4 | semidirect |
| 25. #4681 | C4 | semidirect |
| 36. #1274 | D3 | semidirect |
| 350. C3 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79304 | 2 |
| #79290 | 2 |
| #70765 | 2 |
| #69432 | 2 |
| C3×#1274 | 2 |
| #67747 | 2 |
| #9281 | 3 |