Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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. #79337 | C2 | semidirect |
| 3. C3×#1536 | C2 | semidirect |
| 4. #71813 | C2 | semidirect |
| 5. #70835 | C2 | semidirect |
| 6. #67753 | C2 | semidirect |
| 7. #67752 | C2 | semidirect |
| 13. #5088 | C4 | semidirect |
| 14. #5080 | C4 | semidirect |
| 15. #5073 | C4 | semidirect |
| 16. #5070 | C4 | semidirect |
| 30. #1536 | D3 | semidirect |
| 328. C3 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83295 | 2 |
| #79337 | 2 |
| C3×#1536 | 2 |
| #71813 | 2 |
| #70835 | 2 |
| #67753 | 2 |
| #67752 | 2 |
| #9417 | 3 |