Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. Q8×Dic106 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810968 | C2 | semidirect |
| 5. #16810913 | C2 | semidirect |
| 6. #16810912 | C2 | semidirect |
| 7. #16810823 | C2 | semidirect |
| 8. #16810821 | C2 | semidirect |
| 9. C8×Dic106 | C2 | semidirect |
| 10. #16810708 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 77. Q8×C53 | #41 | semidirect |
| 99. Dic106 | SD16 | semidirect |
| 136. C4×SD16 | D53 | semidirect |
| 137. C53 | #3362 | semidirect |
| 206. Q8 | #11719945 | semidirect |