Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 113 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×#1492 | C2 | semidirect |
| 3. #71815 | C2 | semidirect |
| 4. #70512 | C2 | semidirect |
| 5. #70490 | C2 | semidirect |
| 6. #69750 | C2 | semidirect |
| 7. #69735 | C2 | semidirect |
| 15. #5088 | C4 | semidirect |
| 16. #5078 | C4 | semidirect |
| 17. #5073 | C4 | semidirect |
| 18. #5070 | C4 | semidirect |
| 34. #1492 | D3 | semidirect |
| 344. C3 | #9852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83291 | 2 |
| C3×#1492 | 2 |
| #71815 | 2 |
| #70512 | 2 |
| #70490 | 2 |
| #69750 | 2 |
| #69735 | 2 |
| #9852 | 3 |