Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 289 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. #16811390 | C2 | semidirect |
| 2. #41×Dic53 | C2 | semidirect |
| 3. #16810640 | C2 | semidirect |
| 4. C2×#13133144 | C2 | semidirect |
| 7. C2×#11719917 | C22 | semidirect |
| 10. #13133176 | C22 | semidirect |
| 11. C2×C4×Dic53 | C22 | semidirect |
| 12. #13133144 | C22 | semidirect |
| 13. #13133144 | C22 | semidirect |
| 15. 2−1+4×C53 | C4 | semidirect |
| 17. H(5,𝔽2)×C53 | C4 | semidirect |
| 26. #41×C53 | C2×C4 | semidirect |
| 30. C2×Q8×C53 | C2×C4 | semidirect |
| 34. C2×D4×C53 | C2×C4 | semidirect |
| 89. C53 | #2901 | semidirect |
| 91. 2−1+4 | Dic53 | semidirect |
| 93. H(5,𝔽2) | Dic53 | semidirect |
| 110. #41 | C2×Dic53 | semidirect |
| 114. C2×Q8 | C2×Dic53 | semidirect |
| 118. C2×D4 | C2×Dic53 | semidirect |