Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. C3×C42×C8 | C2 | semidirect |
| 3. #69735 | C2 | semidirect |
| 4. #69731 | C2 | semidirect |
| 5. #69395 | C2 | semidirect |
| 15. #4695 | C4 | semidirect |
| 16. #4694 | C4 | semidirect |
| 18. #4682 | C4 | semidirect |
| 23. C42×C8 | D3 | semidirect |
| 87. C3×C42 | D8 | semidirect |
| 151. C3×C8 | #104 | semidirect |
| 180. C42 | D24 | semidirect |
| 227. C8 | #805 | semidirect |
| 249. C3 | #9844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×C42×C8 | 2 |
| #69735 | 2 |
| #69731 | 2 |
| #69395 | 2 |
| #9844 | 3 |