Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16811336 | C2 | semidirect |
| 2. #16811027 | C2 | semidirect |
| 3. #16810949 | C2 | semidirect |
| 4. #16810947 | C2 | semidirect |
| 5. #16810912 | C2 | semidirect |
| 6. #16810860 | C2 | semidirect |
| 7. #16810859 | C2 | semidirect |
| 8. #16810705 | C2 | semidirect |
| 9. C8×C22⋊D53 | C2 | semidirect |
| 10. #16810660 | C2 | semidirect |
| 11. C53×#427 | C2 | semidirect |
| 131. #427 | D53 | semidirect |
| 132. C53 | #3341 | semidirect |