Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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. #16811058 | C2 | semidirect |
| 2. C2×#13133160 | C2 | semidirect |
| 3. #16810893 | C2 | semidirect |
| 4. #16810439 | C2 | semidirect |
| 5. #16810430 | C2 | semidirect |
| 6. #16810407 | C2 | semidirect |
| 7. C53×#578 | C2 | semidirect |
| 91. #578 | D53 | semidirect |
| 98. C53 | #2193 | semidirect |