Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
554 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 131 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×#1567 | C2 | semidirect |
| 3. #70512 | C2 | semidirect |
| 4. #70498 | C2 | semidirect |
| 5. C4×C8×Dic3 | C2 | semidirect |
| 15. #4695 | C4 | semidirect |
| 16. #4694 | C4 | semidirect |
| 18. #4682 | C4 | semidirect |
| 24. #1567 | D3 | semidirect |
| 95. C4×Dic3 | D8 | semidirect |
| 151. C3×C8 | #104 | semidirect |
| 227. C8 | #825 | 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×#1567 | 2 |
| #70512 | 2 |
| #70498 | 2 |
| C4×C8×Dic3 | 2 |
| #9844 | 3 |