Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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. #83280 | C2 | semidirect |
| 3. #71812 | C2 | semidirect |
| 4. #71812 | C2 | semidirect |
| 5. #71803 | C2 | semidirect |
| 6. #67747 | C2 | semidirect |
| 7. #67737 | C2 | semidirect |
| 11. C3×#493 | C4 | semidirect |
| 12. C3×#492 | C4 | semidirect |
| 13. C3×#487 | C4 | semidirect |
| 14. C3×#486 | C4 | semidirect |
| 81. #493 | Dic3 | semidirect |
| 82. #492 | Dic3 | semidirect |
| 83. #487 | Dic3 | semidirect |
| 84. #486 | Dic3 | semidirect |
| 350. C3 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3207 | 2 |
| #83280 | 2 |
| #71812 | 2 |
| #71803 | 2 |
| #67747 | 2 |
| #67737 | 2 |
| #9281 | 3 |