Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811273 | C2 | semidirect |
| 2. #16811027 | C2 | semidirect |
| 3. #16810935 | C2 | semidirect |
| 4. #16810934 | C2 | semidirect |
| 5. #16810901 | C2 | semidirect |
| 6. #16810856 | C2 | semidirect |
| 7. D8×Dic53 | C2 | semidirect |
| 8. C8×C22⋊D53 | C2 | semidirect |
| 9. C2×#13133151 | C2 | semidirect |
| 10. #107×D53 | C2 | semidirect |
| 11. C53×#466 | C2 | semidirect |
| 82. C22⋊D53 | D8 | semidirect |
| 95. C8×C53 | #41 | semidirect |
| 130. #466 | D53 | semidirect |
| 135. C53 | #3334 | semidirect |
| 221. C8 | #11719947 | semidirect |