Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 127 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×#1566 | C2 | semidirect |
| 3. #70512 | C2 | semidirect |
| 4. #70498 | C2 | semidirect |
| 5. C4×#815 | C2 | semidirect |
| 15. #4695 | C4 | semidirect |
| 16. #4694 | C4 | semidirect |
| 18. #4682 | C4 | semidirect |
| 24. #1566 | D3 | semidirect |
| 149. C3×C8 | #104 | semidirect |
| 222. C8 | #825 | semidirect |
| 243. C3 | #9849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×#1566 | 2 |
| #70512 | 2 |
| #70498 | 2 |
| C4×#815 | 2 |
| #9849 | 3 |