Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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×#1530 | C2 | semidirect |
| 3. #71812 | C2 | semidirect |
| 4. #70832 | C2 | semidirect |
| 5. #70794 | C2 | semidirect |
| 6. #69806 | C2 | semidirect |
| 7. #69798 | C2 | semidirect |
| 13. #5088 | C4 | semidirect |
| 14. #5078 | C4 | semidirect |
| 15. #5073 | C4 | semidirect |
| 16. #5070 | C4 | semidirect |
| 36. #1530 | D3 | semidirect |
| 362. C3 | #9764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83291 | 2 |
| C3×#1530 | 2 |
| #71812 | 2 |
| #70832 | 2 |
| #70794 | 2 |
| #69806 | 2 |
| #69798 | 2 |
| #9764 | 3 |