Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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. #16811459 | C2 | semidirect |
| 2. #16811434 | C2 | semidirect |
| 3. #16811426 | C2 | semidirect |
| 4. #16811421 | C2 | semidirect |
| 5. C2×#13133243 | C2 | semidirect |
| 6. #16811390 | C2 | semidirect |
| 7. C2×H(5,𝔽2)×C53 | C2 | semidirect |
| 9. #13133264 | C22 | semidirect |
| 10. #13133263 | C22 | semidirect |
| 12. C2×#11719945 | C22 | semidirect |
| 14. #13133248 | C22 | semidirect |
| 15. #13133247 | C22 | semidirect |
| 16. #13133243 | C22 | semidirect |
| 17. #13133243 | C22 | semidirect |
| 18. #13133242 | C22 | semidirect |
| 19. #13133237 | C22 | semidirect |
| 20. C2×#11719923 | C22 | semidirect |
| 21. C2×#11719922 | C22 | semidirect |
| 22. #13133224 | C22 | semidirect |
| 23. C2×#11719917 | C22 | semidirect |
| 25. H(5,𝔽2)×C53 | C22 | semidirect |
| 28. C2×#41×C53 | C22 | semidirect |
| 30. C22×D4×C53 | C22 | semidirect |
| 56. #11719945 | C23 | semidirect |
| 57. C2×D212 | C23 | semidirect |
| 59. C2×Dic106 | C23 | semidirect |
| 60. #11719925 | C23 | semidirect |
| 61. #11719924 | C23 | semidirect |
| 62. #11719923 | C23 | semidirect |
| 63. #11719922 | C23 | semidirect |
| 65. #11719917 | C23 | semidirect |
| 66. C2×#88322 | C23 | semidirect |
| 116. C2×H(5,𝔽2) | D53 | semidirect |
| 122. C53 | #3585 | semidirect |
| 128. H(5,𝔽2) | C2×D53 | semidirect |
| 133. C2×#41 | C2×D53 | semidirect |
| 135. C22×D4 | C2×D53 | semidirect |