Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 99 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. #83333 | C2 | semidirect |
| 3. #71837 | C2 | semidirect |
| 6. #67670 | C2 | semidirect |
| 7. #67666 | C2 | semidirect |
| 11. C3×#500 | C4 | semidirect |
| 12. C3×#492 | C4 | semidirect |
| 13. C3×#487 | C4 | semidirect |
| 14. C3×#486 | C4 | semidirect |
| 77. #500 | Dic3 | semidirect |
| 78. #492 | Dic3 | semidirect |
| 79. #487 | Dic3 | semidirect |
| 80. #486 | Dic3 | semidirect |
| 305. C3 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3182 | 2 |
| #83333 | 2 |
| #71837 | 2 |
| #71813 | 2 |
| #71799 | 2 |
| #67670 | 2 |
| #67666 | 2 |
| #9418 | 3 |