Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#13133250 | C2 | semidirect |
| 3. C2×#13133215 | C2 | semidirect |
| 4. #16810808 | C2 | direct (N × H) |
| 5. C2×#13133143 | C2 | semidirect |
| 6. C2×#101×C53 | C2 | semidirect |
| 16. #13133250 | C22 | semidirect |
| 20. #13133215 | C22 | semidirect |
| 23. #13133143 | C22 | semidirect |
| 26. #101×C53 | C22 | semidirect |
| 110. C2×C53 | #456 | semidirect |
| 118. C2×#101 | D53 | semidirect |
| 119. C53 | C2×#456 | semidirect |
| 139. #101 | C2×D53 | semidirect |
| 223. C2 | #16810808 | direct (N × H) |