Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #16811425 | C2 | semidirect |
| 2. C2×#13133158 | C2 | semidirect |
| 3. #16810890 | C2 | semidirect |
| 4. #16810437 | C2 | semidirect |
| 5. #16810430 | C2 | semidirect |
| 6. #16810408 | C2 | semidirect |
| 7. C53×#509 | C2 | semidirect |
| 17. C2×#11719908 | C22 | semidirect |
| 18. #13133153 | C22 | semidirect |
| 21. C2×D8×C53 | C22 | semidirect |
| 24. M32×C53 | C22 | semidirect |
| 95. #509 | D53 | semidirect |
| 101. C53 | #2192 | semidirect |
| 110. C2×D8 | C2×D53 | semidirect |
| 115. M32 | C2×D53 | semidirect |