Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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. #16811096 | C2 | semidirect |
| 3. #16810595 | C2 | semidirect |
| 4. C2×#13133132 | C2 | semidirect |
| 5. C2×#13133131 | C2 | semidirect |
| 6. #99×D53 | C2 | semidirect |
| 7. C2×#99×C53 | C2 | semidirect |
| 10. C2×#11719945 | C4 | semidirect |
| 11. C2×#11719947 | C4 | semidirect |
| 13. C22×C22⋊D53 | C4 | semidirect |
| 16. C2×D4×D53 | C4 | semidirect |
| 20. #13133173 | C22 | semidirect |
| 21. C2×C22⋊Dic53 | C22 | semidirect |
| 22. C22⋊C4×D53 | C22 | semidirect |
| 23. #13133132 | C22 | semidirect |
| 24. #13133131 | C22 | semidirect |
| 26. C2×C22⋊C4×C53 | C22 | semidirect |
| 27. #99×C53 | C22 | semidirect |
| 28. C24×C53 | C2×C4 | semidirect |
| 30. C23×D53 | C2×C4 | semidirect |
| 31. C23×D53 | C2×C4 | semidirect |
| 35. C2×D4×C53 | C2×C4 | semidirect |
| 38. C22×C4×C53 | C2×C4 | semidirect |
| 45. C2×C22⋊D53 | C2×C4 | semidirect |
| 46. C2×C22⋊D53 | C2×C4 | semidirect |
| 47. C2×C22⋊D53 | C2×C4 | semidirect |
| 52. C22×Dic53 | C2×C4 | semidirect |
| 53. C22×Dic53 | C2×C4 | semidirect |
| 61. C2×D212 | C2×C4 | semidirect |
| 63. C2×C4×D53 | C2×C4 | semidirect |
| 64. C2×C4×D53 | C2×C4 | semidirect |
| 65. C2×Dic106 | C2×C4 | semidirect |
| 160. C2×#99 | D53 | semidirect |
| 161. C53 | #2883 | semidirect |
| 178. C2×C22⋊C4 | C2×D53 | semidirect |
| 181. #99 | C2×D53 | semidirect |
| 185. C24 | C4×D53 | semidirect |
| 209. C2×D4 | C4×D53 | semidirect |
| 219. C22×C4 | C4×D53 | semidirect |