Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133242 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16811009 | C2 | semidirect |
| 5. #16811008 | C2 | semidirect |
| 6. #16810998 | C2 | semidirect |
| 7. #16810578 | C2 | semidirect |
| 8. C2×#135×C53 | C2 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 15. C2×#11719922 | C22 | semidirect |
| 17. #13133213 | C22 | semidirect |
| 18. #13133206 | C22 | semidirect |
| 22. #13133127 | C22 | semidirect |
| 23. C8×Dic53 | C22 | semidirect |
| 26. C2×Q16×C53 | C22 | semidirect |
| 27. C2×SD16×C53 | C22 | semidirect |
| 28. C2×D8×C53 | C22 | semidirect |
| 46. C2×C8×C53 | D4 | semidirect |
| 55. #11719917 | D4 | semidirect |
| 103. C2×#135 | D53 | semidirect |
| 110. C53 | #3155 | semidirect |
| 115. C2×Q16 | C2×D53 | semidirect |
| 117. C2×SD16 | C2×D53 | semidirect |
| 122. C2×D8 | C2×D53 | semidirect |
| 154. C2×C8 | C22⋊D53 | semidirect |