Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 89 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. #78481 | C2 | semidirect |
| 3. #69798 | C2 | semidirect |
| 4. #69545 | C2 | semidirect |
| 5. #69544 | C2 | semidirect |
| 6. C3×#1295 | C2 | semidirect |
| 7. #67662 | C2 | semidirect |
| 20. #4714 | C4 | semidirect |
| 21. #4713 | C4 | semidirect |
| 22. #4712 | C4 | semidirect |
| 28. #4702 | C4 | semidirect |
| 42. #1295 | D3 | semidirect |
| 409. C3 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78500 | 2 |
| #78481 | 2 |
| #69798 | 2 |
| #69545 | 2 |
| #69544 | 2 |
| C3×#1295 | 2 |
| #67662 | 2 |
| #9432 | 3 |