Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #16811664 | C2 | semidirect |
| 3. D8×#6157 | C2 | semidirect |
| 4. #16811633 | C2 | semidirect |
| 5. #16811615 | C2 | semidirect |
| 6. #16811586 | C2 | semidirect |
| 10. D4×#6157 | C22 | semidirect |
| 14. #13133286 | C22 | semidirect |
| 15. #13133285 | C22 | semidirect |
| 16. #13133279 | C22 | semidirect |
| 17. #13133271 | C22 | semidirect |
| 18. C8×#6157 | C22 | semidirect |
| 20. C2×D424 | C4 | semidirect |
| 21. C2×#11719922 | C4 | semidirect |
| 22. D8×D53 | C4 | semidirect |
| 23. D8×D53 | C4 | semidirect |
| 27. C2×D8×C53 | C4 | semidirect |
| 30. C2×D4×C53 | C2×C4 | semidirect |
| 34. D4×D53 | C2×C4 | semidirect |
| 36. C2×D212 | C2×C4 | semidirect |
| 48. D8×C53 | C2×C4 | semidirect |
| 49. D8×C53 | C2×C4 | semidirect |
| 50. C2×C8×C53 | C2×C4 | semidirect |
| 51. #11719922 | C2×C4 | semidirect |
| 52. #11719922 | C2×C4 | semidirect |
| 53. C2×#88322 | C2×C4 | semidirect |
| 54. D424 | C2×C4 | semidirect |
| 55. D424 | C2×C4 | semidirect |
| 56. C8×D53 | C2×C4 | semidirect |
| 57. C8×D53 | C2×C4 | semidirect |
| 116. C53 | #2948 | semidirect |
| 124. C2×D8 | #6157 | semidirect |
| 144. C2×D4 | C2×#6157 | semidirect |
| 151. D8 | C2×#6157 | semidirect |
| 152. D8 | C2×#6157 | semidirect |
| 161. C2×C8 | C2×#6157 | semidirect |