Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #79286 | C2 | semidirect |
| 3. #70758 | C2 | semidirect |
| 4. #69556 | C2 | semidirect |
| 5. #69545 | C2 | semidirect |
| 6. C3×#1286 | C2 | semidirect |
| 7. #67714 | C2 | semidirect |
| 20. #4843 | C4 | semidirect |
| 21. #4841 | C4 | semidirect |
| 34. #1286 | D3 | semidirect |
| 381. C3 | #9305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79286 | 2 |
| #79055 | 2 |
| #70758 | 2 |
| #69556 | 2 |
| #69545 | 2 |
| C3×#1286 | 2 |
| #67714 | 2 |
| #9305 | 3 |