Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 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. #16811098 | C2 | semidirect |
| 2. #16810735 | C2 | semidirect |
| 3. D8×Dic53 | C2 | semidirect |
| 4. #16810661 | C2 | semidirect |
| 5. #16810628 | C2 | semidirect |
| 6. #16810578 | C2 | semidirect |
| 10. D4×Dic53 | C22 | semidirect |
| 14. #13133151 | C22 | semidirect |
| 15. #13133149 | C22 | semidirect |
| 16. #13133138 | C22 | semidirect |
| 17. #13133127 | C22 | semidirect |
| 18. C8×Dic53 | C22 | semidirect |
| 20. C2×D8×C53 | C4 | semidirect |
| 27. C2×D4×C53 | C2×C4 | semidirect |
| 31. D8×C53 | C2×C4 | semidirect |
| 32. D8×C53 | C2×C4 | semidirect |
| 33. C2×C8×C53 | C2×C4 | semidirect |
| 85. C53 | #2948 | semidirect |
| 87. C2×D8 | Dic53 | semidirect |
| 105. C2×D4 | C2×Dic53 | semidirect |
| 109. D8 | C2×Dic53 | semidirect |
| 110. D8 | C2×Dic53 | semidirect |
| 113. C2×C8 | C2×Dic53 | semidirect |