Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 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. #78537 | C2 | semidirect |
| 4. #70769 | C2 | semidirect |
| 5. #70524 | C2 | semidirect |
| 7. C3×#1299 | C2 | semidirect |
| 38. #1299 | D3 | semidirect |
| 349. C3 | #10114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79312 | 2 |
| #79065 | 2 |
| #78537 | 2 |
| #70769 | 2 |
| #70524 | 2 |
| #69859 | 2 |
| C3×#1299 | 2 |
| #10114 | 3 |