Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D53⋊#131 | C2 | semidirect |
| 2. #16811692 | C2 | semidirect |
| 3. #16811615 | C2 | semidirect |
| 4. #16811614 | C2 | semidirect |
| 5. #16811613 | C2 | semidirect |
| 6. C2×#13133279 | C2 | semidirect |
| 10. D53⋊M16 | C22 | semidirect |
| 11. C2×D53⋊C8 | C22 | semidirect |
| 14. #13133296 | C22 | semidirect |
| 15. C2×C4⋊#6157 | C22 | semidirect |
| 16. #13133280 | C22 | semidirect |
| 17. #13133280 | C22 | semidirect |
| 18. #13133279 | C22 | semidirect |
| 19. #13133279 | C22 | semidirect |
| 20. #13133279 | C22 | semidirect |
| 22. #13133263 | C4 | semidirect |
| 23. #13133263 | C4 | semidirect |
| 25. #13133262 | C4 | semidirect |
| 31. H(5,𝔽2)×C53 | C4 | semidirect |
| 36. #41×C53 | C2×C4 | semidirect |
| 38. C2×D4×C53 | C2×C4 | semidirect |
| 42. #11719949 | C2×C4 | semidirect |
| 48. #11719947 | C2×C4 | semidirect |
| 56. D4×D53 | C2×C4 | semidirect |
| 62. #11719945 | C2×C4 | semidirect |
| 64. C2×D212 | C2×C4 | semidirect |
| 154. C53 | #2897 | semidirect |
| 160. H(5,𝔽2) | #6157 | semidirect |
| 193. #41 | C2×#6157 | semidirect |
| 210. C2×D4 | C2×#6157 | semidirect |