Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16810640 | C2 | semidirect |
| 2. #16810632 | C2 | semidirect |
| 3. #16810607 | C2 | semidirect |
| 4. #16810597 | C2 | semidirect |
| 17. C2×#41×C53 | C4 | semidirect |
| 21. C22×Q8×C53 | C4 | semidirect |
| 114. C53 | #1796 | semidirect |
| 119. C2×#41 | Dic53 | semidirect |
| 123. C22×Q8 | Dic53 | semidirect |