Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #16810664 | C2 | direct (N × H) |
| 5. C2×#13133150 | C2 | semidirect |
| 6. C2×#13133149 | C2 | semidirect |
| 7. C2×#13133148 | C2 | semidirect |
| 8. C2×#107×C53 | C2 | semidirect |
| 11. C2×#11719912 | C4 | semidirect |
| 23. #13133150 | C22 | semidirect |
| 24. #13133149 | C22 | semidirect |
| 25. #13133148 | C22 | semidirect |
| 29. #107×C53 | C22 | semidirect |
| 43. C2×C8×C53 | C2×C4 | semidirect |
| 56. C2×#88322 | C2×C4 | semidirect |
| 58. #11719912 | C2×C4 | semidirect |
| 82. C8×C53 | C22×C4 | semidirect |
| 83. #88322 | C22×C4 | semidirect |
| 101. C2×C53 | #428 | semidirect |
| 111. C2×#107 | D53 | semidirect |
| 114. C53 | C2×#428 | semidirect |
| 133. #107 | C2×D53 | semidirect |
| 152. C2×C8 | C4×D53 | semidirect |
| 189. C8 | C2×C4×D53 | semidirect |
| 207. C2 | #16810664 | direct (N × H) |