Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×#1506 | C2 | semidirect |
| 3. #71822 | C2 | semidirect |
| 5. #70794 | C2 | semidirect |
| 6. #69434 | C2 | semidirect |
| 13. #5088 | C4 | semidirect |
| 14. #5085 | C4 | semidirect |
| 15. #5080 | C4 | semidirect |
| 16. #5079 | C4 | semidirect |
| 37. #1506 | D3 | semidirect |
| 351. C3 | #9761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83343 | 2 |
| C3×#1506 | 2 |
| #71822 | 2 |
| #70806 | 2 |
| #70794 | 2 |
| #69434 | 2 |
| #69432 | 2 |
| #9761 | 3 |