Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #16811428 | C2 | semidirect |
| 2. #16811061 | C2 | semidirect |
| 3. C2×D848 | C2 | semidirect |
| 4. #16810893 | C2 | semidirect |
| 5. #16810437 | C2 | semidirect |
| 6. #16810431 | C2 | semidirect |
| 7. C53×#350 | C2 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 20. #13133153 | C22 | semidirect |
| 23. M32×C53 | C22 | semidirect |
| 24. C2×C16×C53 | C22 | semidirect |
| 100. #350 | D53 | semidirect |
| 101. C53 | #2192 | semidirect |
| 115. M32 | C2×D53 | semidirect |
| 116. C2×C16 | C2×D53 | semidirect |