Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×Q16×D53 | C2 | semidirect |
| 3. C2×#13133162 | C2 | semidirect |
| 4. C2×#13133161 | C2 | semidirect |
| 5. C2×#13133160 | C2 | semidirect |
| 6. SD32×D53 | C2 | direct (N × H) |
| 7. C2×C16×D53 | C2 | semidirect |
| 8. C2×SD32×C53 | C2 | semidirect |
| 11. C2×Dic212 | C22 | semidirect |
| 14. Q16×D53 | C22 | semidirect |
| 20. #13133162 | C22 | semidirect |
| 21. #13133161 | C22 | semidirect |
| 22. #13133160 | C22 | semidirect |
| 23. C2×#11719908 | C22 | semidirect |
| 24. C16×D53 | C22 | semidirect |
| 25. C2×Q16×C53 | C22 | semidirect |
| 27. SD32×C53 | C22 | semidirect |
| 28. C2×C16×C53 | C22 | semidirect |
| 43. Q16×C53 | C23 | semidirect |
| 51. Dic212 | C23 | semidirect |
| 56. C16×C53 | C23 | semidirect |
| 57. #11719908 | C23 | semidirect |
| 89. C2×D53 | SD32 | direct (N × H) |
| 98. C2×C53 | C2×SD32 | semidirect |
| 101. D53 | C2×SD32 | direct (N × H) |
| 108. C2×SD32 | D53 | direct (N × H) |
| 110. C53 | C22×SD32 | semidirect |
| 117. C2×Q16 | C2×D53 | semidirect |
| 127. SD32 | C2×D53 | direct (N × H) |
| 130. C2×C16 | C2×D53 | semidirect |
| 148. Q16 | C22×D53 | semidirect |
| 159. C16 | C22×D53 | semidirect |
| 201. C2 | SD32×D53 | direct (N × H) |