Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13133209 | C2 | semidirect |
| 3. #16810924 | C2 | direct (N × H) |
| 4. C2×#13133151 | C2 | semidirect |
| 5. C2×#13133149 | C2 | semidirect |
| 8. C2×C4⋊C8×C53 | C2 | semidirect |
| 12. #13133209 | C22 | semidirect |
| 21. #13133151 | C22 | semidirect |
| 22. #13133149 | C22 | semidirect |
| 28. C4⋊C8×C53 | C22 | semidirect |
| 99. C2×C53 | #478 | semidirect |
| 109. C2×C4⋊C8 | D53 | semidirect |
| 112. C53 | C2×#478 | semidirect |
| 130. C4⋊C8 | C2×D53 | semidirect |
| 203. C2 | #16810924 | direct (N × H) |