Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 97 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. #79289 | C2 | semidirect |
| 3. C3×#1484 | C2 | semidirect |
| 4. #71801 | C2 | semidirect |
| 5. #69859 | C2 | semidirect |
| 6. #67739 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 36. #1484 | D3 | semidirect |
| 388. C3 | #9069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83285 | 2 |
| #79289 | 2 |
| C3×#1484 | 2 |
| #71801 | 2 |
| #69859 | 2 |
| #67739 | 2 |
| #67667 | 2 |
| #9069 | 3 |