Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #71812 | C2 | semidirect |
| 3. #71798 | C2 | semidirect |
| 4. #69751 | C2 | semidirect |
| 5. #69732 | C2 | semidirect |
| 8. C3×#500 | C4 | semidirect |
| 9. C3×#493 | C4 | semidirect |
| 10. C3×#486 | C4 | semidirect |
| 61. #500 | Dic3 | semidirect |
| 62. #493 | Dic3 | semidirect |
| 63. #486 | Dic3 | semidirect |
| 269. C3 | #9764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3169 | 2 |
| #71812 | 2 |
| #71798 | 2 |
| #69751 | 2 |
| #69732 | 2 |
| #9764 | 3 |