Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #78510 | C2 | semidirect |
| 3. #69853 | C2 | semidirect |
| 4. #69565 | C2 | semidirect |
| 5. #69564 | C2 | semidirect |
| 6. C3×#1288 | C2 | semidirect |
| 7. #67756 | C2 | semidirect |
| 22. #4715 | C4 | semidirect |
| 23. #4713 | C4 | semidirect |
| 24. #4712 | C4 | semidirect |
| 26. #4703 | C4 | semidirect |
| 41. #1288 | D3 | semidirect |
| 402. C3 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79354 | 2 |
| #78510 | 2 |
| #69853 | 2 |
| #69565 | 2 |
| #69564 | 2 |
| C3×#1288 | 2 |
| #67756 | 2 |
| #9370 | 3 |