Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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×D424 | C2 | semidirect |
| 2. D4×D212 | C2 | semidirect |
| 3. #16811000 | C2 | semidirect |
| 4. #16810859 | C2 | semidirect |
| 5. #16810819 | C2 | semidirect |
| 6. #16810759 | C2 | semidirect |
| 7. C4×D424 | C2 | semidirect |
| 8. C8×D4×C53 | C2 | semidirect |
| 9. C22×D212 | C22 | semidirect |
| 13. C2×D424 | C22 | semidirect |
| 14. C2×D424 | C22 | semidirect |
| 15. C2×D424 | C22 | semidirect |
| 16. #13133214 | C22 | semidirect |
| 18. #13133191 | C22 | semidirect |
| 20. C4×D212 | C22 | semidirect |
| 21. #13133151 | C22 | semidirect |
| 22. #13133139 | C22 | semidirect |
| 23. #13133139 | C22 | semidirect |
| 24. C22×C8×C53 | C22 | semidirect |
| 26. C4⋊C8×C53 | C22 | semidirect |
| 27. C22⋊C8×C53 | C22 | semidirect |
| 28. C4×C8×C53 | C22 | semidirect |
| 55. D424 | D4 | direct (N × H) |
| 62. D4×C53 | D8 | semidirect |
| 77. D212 | C2×D4 | semidirect |
| 81. C8×C53 | C2×D4 | semidirect |
| 84. C22×C53 | C2×D8 | semidirect |
| 95. C4×C53 | C2×D8 | semidirect |
| 113. C8×D4 | D53 | semidirect |
| 114. C53 | D4×D8 | semidirect |
| 122. C22×C8 | C2×D53 | semidirect |
| 130. C4⋊C8 | C2×D53 | semidirect |
| 133. C22⋊C8 | C2×D53 | semidirect |
| 134. C4×C8 | C2×D53 | semidirect |
| 176. D4 | D424 | direct (N × H) |
| 187. C8 | D4×D53 | semidirect |
| 197. C22 | C2×D424 | semidirect |
| 202. C4 | C2×D424 | semidirect |