Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. C2×#13133134 | C2 | semidirect |
| 3. #16810409 | C2 | direct (N × H) |
| 4. C2×#99×C53 | C2 | semidirect |
| 5. C24×D53 | C4 | semidirect |
| 10. #13133185 | C4 | semidirect |
| 12. C2×C22⋊Dic53 | C4 | semidirect |
| 15. #13133134 | C22 | semidirect |
| 19. #99×C53 | C22 | semidirect |
| 27. C23×D53 | C2×C4 | semidirect |
| 43. C22⋊Dic53 | C2×C4 | semidirect |
| 122. C2×C53 | AΣL(1,𝔽16) | semidirect |
| 127. C2×#99 | D53 | semidirect |
| 129. C53 | C2×AΣL(1,𝔽16) | semidirect |
| 144. #99 | C2×D53 | semidirect |
| 247. C2 | #16810409 | direct (N × H) |