Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 3. #70813 | C2 | semidirect |
| 5. #69856 | C2 | semidirect |
| 6. C3×#1291 | C2 | semidirect |
| 7. #67751 | C2 | semidirect |
| 38. #1291 | D3 | semidirect |
| 357. C3 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79348 | 2 |
| #78520 | 2 |
| #70813 | 2 |
| #70798 | 2 |
| #69856 | 2 |
| C3×#1291 | 2 |
| #67751 | 2 |
| #9314 | 3 |