Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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. #70515 | C2 | semidirect |
| 5. #69546 | C2 | semidirect |
| 6. C3×#1286 | C2 | semidirect |
| 7. #67737 | C2 | semidirect |
| 20. #4694 | C4 | semidirect |
| 21. #4693 | C4 | semidirect |
| 33. #1286 | D3 | semidirect |
| 58. #869 | C2×C4 | semidirect |
| 59. #869 | C2×C4 | semidirect |
| 66. C3×C4×C8 | C2×C4 | semidirect |
| 142. C4×Dic3 | SD16 | semidirect |
| 180. C4×C8 | C4×D3 | semidirect |
| 382. C3 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79305 | 2 |
| #74153 | 2 |
| #70515 | 2 |
| #70502 | 2 |
| #69546 | 2 |
| C3×#1286 | 2 |
| #67737 | 2 |
| #9295 | 3 |