Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 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×#13133134 | C2 | semidirect |
| 2. C2×#13133132 | C2 | semidirect |
| 3. #16810410 | C2 | direct (N × H) |
| 8. #13133134 | C22 | semidirect |
| 10. #13133132 | C22 | semidirect |
| 11. C25×C53 | C4 | semidirect |
| 16. #120×C53 | C4 | semidirect |
| 19. C2×C22⋊C4×C53 | C4 | semidirect |
| 26. C24×C53 | C2×C4 | semidirect |
| 43. C22⋊C4×C53 | C2×C4 | semidirect |
| 123. C2×C53 | AΣL(1,𝔽16) | semidirect |
| 129. C53 | C2×AΣL(1,𝔽16) | semidirect |
| 130. C25 | Dic53 | semidirect |
| 136. #120 | Dic53 | semidirect |
| 140. C2×C22⋊C4 | Dic53 | semidirect |
| 151. C24 | C2×Dic53 | semidirect |
| 173. C22⋊C4 | C2×Dic53 | semidirect |
| 247. C2 | #16810410 | direct (N × H) |