Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16810989 | C2 | semidirect |
| 3. #16810971 | C2 | semidirect |
| 4. #16810920 | C2 | semidirect |
| 5. #16810900 | C2 | semidirect |
| 6. #16810823 | C2 | semidirect |
| 7. #16810823 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 9. #16810721 | C2 | semidirect |
| 10. C4×#11719924 | C2 | semidirect |
| 11. C53×#557 | C2 | semidirect |
| 79. Q8×C53 | #41 | semidirect |
| 125. #557 | D53 | semidirect |
| 136. C53 | #3368 | semidirect |
| 204. Q8 | #11719949 | semidirect |