Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1720 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×#11719949 | C2 | semidirect |
| 2. C22×D4×D53 | C2 | semidirect |
| 3. C2×#13133244 | C2 | direct (N × H) |
| 4. C22×#11719924 | C2 | semidirect |
| 5. C22×D424 | C2 | semidirect |
| 6. C22×#11719922 | C2 | semidirect |
| 7. C22×#11719912 | C2 | semidirect |
| 8. C22×SD16×C53 | C2 | semidirect |
| 11. C2×#11719949 | C22 | semidirect |
| 14. C22×D212 | C22 | semidirect |
| 17. C2×D4×D53 | C22 | semidirect |
| 20. #13133244 | C22 | direct (N × H) |
| 21. C2×#11719924 | C22 | semidirect |
| 22. C2×D424 | C22 | semidirect |
| 23. C2×#11719922 | C22 | semidirect |
| 24. C2×#11719912 | C22 | semidirect |
| 25. C22×#88322 | C22 | semidirect |
| 26. C22×Q8×C53 | C22 | semidirect |
| 28. C2×SD16×C53 | C22 | semidirect |
| 29. C22×C8×C53 | C22 | semidirect |
| 37. C2×Q8×C53 | C23 | semidirect |
| 45. #11719949 | C23 | semidirect |
| 47. D4×D53 | C23 | semidirect |
| 52. C2×D212 | C23 | semidirect |
| 56. SD16×C53 | C23 | semidirect |
| 57. C2×C8×C53 | C23 | semidirect |
| 58. #11719924 | C23 | semidirect |
| 59. #11719922 | C23 | semidirect |
| 60. C2×#88322 | C23 | semidirect |
| 61. D424 | C23 | semidirect |
| 62. #11719912 | C23 | semidirect |
| 75. Q8×C53 | C24 | semidirect |
| 87. D212 | C24 | semidirect |
| 91. C8×C53 | C24 | semidirect |
| 92. #88322 | C24 | semidirect |
| 95. C22×C53 | AGL(1,ℤ/8) | semidirect |
| 110. C2×C53 | C2×AGL(1,ℤ/8) | semidirect |
| 119. C22×SD16 | D53 | semidirect |
| 123. C53 | C22×AGL(1,ℤ/8) | semidirect |
| 127. C22×Q8 | C2×D53 | semidirect |
| 139. C2×SD16 | C2×D53 | semidirect |
| 144. C22×C8 | C2×D53 | semidirect |
| 154. C2×Q8 | C22×D53 | semidirect |
| 172. SD16 | C22×D53 | semidirect |
| 177. C2×C8 | C22×D53 | semidirect |
| 190. Q8 | C23×D53 | semidirect |
| 207. C8 | C23×D53 | semidirect |
| 217. C22 | #13133244 | direct (N × H) |
| 227. C2 | C2×#13133244 | direct (N × H) |