Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16811180 | C2 | semidirect |
| 3. #16810983 | C2 | semidirect |
| 4. #16810978 | C2 | semidirect |
| 5. #16810633 | C2 | semidirect |
| 7. C4×M16×C53 | C2 | semidirect |
| 10. #13133217 | C22 | semidirect |
| 11. #13133209 | C22 | semidirect |
| 19. #13133142 | C22 | semidirect |
| 23. #97×C53 | C22 | semidirect |
| 24. C4×C8×C53 | C22 | semidirect |
| 90. C4×M16 | D53 | semidirect |
| 91. C53 | #3140 | semidirect |
| 107. #97 | C2×D53 | semidirect |
| 108. C4×C8 | C2×D53 | semidirect |