Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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. #70741 | C2 | semidirect |
| 3. #70520 | C2 | semidirect |
| 6. C3×#1303 | C2 | semidirect |
| 7. #67619 | C2 | semidirect |
| 20. #4486 | C4 | semidirect |
| 21. #4486 | C4 | semidirect |
| 22. #4485 | C4 | semidirect |
| 23. #4485 | C4 | semidirect |
| 33. #1303 | D3 | semidirect |
| 332. C3 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70772 | 2 |
| #70741 | 2 |
| #70520 | 2 |
| #70498 | 2 |
| #69492 | 2 |
| C3×#1303 | 2 |
| #67619 | 2 |
| #9592 | 3 |