Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 3. #71837 | C2 | semidirect |
| 4. #71825 | C2 | semidirect |
| 6. #67756 | C2 | semidirect |
| 7. #67752 | C2 | semidirect |
| 11. C3×#501 | C4 | semidirect |
| 12. C3×#501 | C4 | semidirect |
| 13. C3×#489 | C4 | semidirect |
| 14. C3×#489 | C4 | semidirect |
| 98. #501 | Dic3 | semidirect |
| 99. #501 | Dic3 | semidirect |
| 100. #489 | Dic3 | semidirect |
| 101. #489 | Dic3 | semidirect |
| 373. C3 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3240 | 2 |
| #83127 | 2 |
| #71837 | 2 |
| #71825 | 2 |
| #71757 | 2 |
| #67756 | 2 |
| #67752 | 2 |
| #9369 | 3 |