Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #16811058 | C2 | semidirect |
| 2. C2×#13133158 | C2 | semidirect |
| 3. #16810893 | C2 | semidirect |
| 4. #16810436 | C2 | semidirect |
| 5. #16810430 | C2 | semidirect |
| 6. #16810407 | C2 | semidirect |
| 7. C53×#576 | C2 | semidirect |
| 9. C2×D424 | C22 | semidirect |
| 13. #13133157 | C22 | semidirect |
| 14. C2×#11719908 | C22 | semidirect |
| 15. #13133153 | C22 | semidirect |
| 94. #576 | D53 | semidirect |
| 101. C53 | #2192 | semidirect |