Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #16811702 | C2 | semidirect |
| 2. #41×#6157 | C2 | semidirect |
| 3. #16811621 | C2 | semidirect |
| 4. #16811620 | C2 | semidirect |
| 5. D53⋊#104 | C2 | semidirect |
| 6. C2×#13133281 | C2 | semidirect |
| 10. C2×#11719936 | C22 | semidirect |
| 11. D53⋊M16 | C22 | semidirect |
| 14. #13133296 | C22 | semidirect |
| 15. C2×C4×#6157 | C22 | semidirect |
| 16. #13133282 | C22 | semidirect |
| 17. #13133282 | C22 | semidirect |
| 18. #13133281 | C22 | semidirect |
| 19. #13133281 | C22 | semidirect |
| 20. #13133281 | C22 | semidirect |
| 22. #13133264 | C4 | semidirect |
| 23. #13133264 | C4 | semidirect |
| 25. #13133262 | C4 | semidirect |
| 31. H(5,𝔽2)×C53 | C4 | semidirect |
| 35. #41×C53 | C2×C4 | semidirect |
| 37. C2×D4×C53 | C2×C4 | semidirect |
| 44. Q8×D53 | C2×C4 | semidirect |
| 52. #11719947 | C2×C4 | semidirect |
| 57. D4×D53 | C2×C4 | semidirect |
| 62. #11719945 | C2×C4 | semidirect |
| 66. C2×Dic106 | C2×C4 | semidirect |
| 147. C53 | #2901 | semidirect |
| 153. H(5,𝔽2) | #6157 | semidirect |
| 189. #41 | C2×#6157 | semidirect |
| 202. C2×D4 | C2×#6157 | semidirect |