Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 424 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. #83127 | C2 | semidirect |
| 3. #71813 | C2 | semidirect |
| 4. #71801 | C2 | semidirect |
| 5. #71757 | C2 | semidirect |
| 6. #67756 | C2 | semidirect |
| 7. #67752 | C2 | semidirect |
| 11. C3×#497 | C4 | semidirect |
| 12. C3×#496 | C4 | semidirect |
| 13. C3×#491 | C4 | semidirect |
| 14. C3×#490 | C4 | semidirect |
| 98. #497 | Dic3 | semidirect |
| 99. #496 | Dic3 | semidirect |
| 100. #491 | Dic3 | semidirect |
| 101. #490 | Dic3 | semidirect |
| 402. C3 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3219 | 2 |
| #83127 | 2 |
| #71813 | 2 |
| #71801 | 2 |
| #71757 | 2 |
| #67756 | 2 |
| #67752 | 2 |
| #9370 | 3 |