Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 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. #41×Dic53 | C2 | semidirect |
| 2. #16810735 | C2 | semidirect |
| 3. #16810730 | C2 | semidirect |
| 4. #16810724 | C2 | semidirect |
| 5. #16810661 | C2 | semidirect |
| 6. #16810619 | C2 | semidirect |
| 7. C2×#13133127 | C2 | semidirect |
| 24. #135×C53 | C4 | semidirect |
| 30. #41×C53 | C2×C4 | semidirect |
| 38. Q16×C53 | C2×C4 | semidirect |
| 39. SD16×C53 | C2×C4 | semidirect |
| 40. D8×C53 | C2×C4 | semidirect |
| 41. C2×C8×C53 | C2×C4 | semidirect |
| 98. C53 | #2943 | semidirect |
| 100. #135 | Dic53 | semidirect |
| 120. #41 | C2×Dic53 | semidirect |
| 128. Q16 | C2×Dic53 | semidirect |
| 129. SD16 | C2×Dic53 | semidirect |
| 130. D8 | C2×Dic53 | semidirect |
| 133. C2×C8 | C2×Dic53 | semidirect |