Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #70501 | C2 | semidirect |
| 5. #69862 | C2 | semidirect |
| 6. C3×#1299 | C2 | semidirect |
| 7. #67739 | C2 | semidirect |
| 37. #1299 | D3 | semidirect |
| 377. C3 | #9214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79302 | 2 |
| #78519 | 2 |
| #70501 | 2 |
| #70497 | 2 |
| #69862 | 2 |
| C3×#1299 | 2 |
| #67739 | 2 |
| #9214 | 3 |