Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
800 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 800 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. #16811690 | C2 | semidirect |
| 2. #16811603 | C2 | semidirect |
| 3. #16811602 | C2 | semidirect |
| 4. D53⋊#99 | C2 | semidirect |
| 5. C2×#13133275 | C2 | semidirect |
| 8. #13133296 | C22 | semidirect |
| 9. C2×C22⋊#6157 | C22 | semidirect |
| 10. #13133276 | C22 | semidirect |
| 11. #13133275 | C22 | semidirect |
| 12. #13133275 | C22 | semidirect |
| 14. C2×#11719945 | C4 | semidirect |
| 16. C2×#11719947 | C4 | semidirect |
| 17. C2×#11719947 | C4 | semidirect |
| 19. C22×C22⋊D53 | C4 | semidirect |
| 21. C2×D4×D53 | C4 | semidirect |
| 24. C22×D4×C53 | C4 | semidirect |
| 25. C24×C53 | C2×C4 | semidirect |
| 26. C23×D53 | C2×C4 | semidirect |
| 31. C2×D4×C53 | C2×C4 | semidirect |
| 32. C2×D4×C53 | C2×C4 | semidirect |
| 33. C22×C4×C53 | C2×C4 | semidirect |
| 37. C2×C22⋊D53 | C2×C4 | semidirect |
| 38. C2×C22⋊D53 | C2×C4 | semidirect |
| 39. C2×C22⋊D53 | C2×C4 | semidirect |
| 40. C2×C22⋊D53 | C2×C4 | semidirect |
| 43. C22×Dic53 | C2×C4 | semidirect |
| 44. C22×Dic53 | C2×C4 | semidirect |
| 55. C2×C4×D53 | C2×C4 | semidirect |
| 56. C2×C4×D53 | C2×C4 | semidirect |
| 58. C2×Dic106 | C2×C4 | semidirect |
| 59. C2×Dic106 | C2×C4 | semidirect |
| 140. C53 | #2883 | semidirect |
| 152. C22×D4 | #6157 | semidirect |
| 161. C24 | C2×#6157 | semidirect |
| 185. C2×D4 | C2×#6157 | semidirect |
| 186. C2×D4 | C2×#6157 | semidirect |
| 193. C22×C4 | C2×#6157 | semidirect |