Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16811277 | C2 | semidirect |
| 2. D4×D212 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810937 | C2 | semidirect |
| 5. #16810904 | C2 | semidirect |
| 6. #16810859 | C2 | semidirect |
| 7. #16810819 | C2 | semidirect |
| 8. #16810759 | C2 | semidirect |
| 9. C4×D424 | C2 | semidirect |
| 10. C2×#13133139 | C2 | semidirect |
| 11. C8×D4×C53 | C2 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 17. #13133217 | C22 | semidirect |
| 23. #13133191 | C22 | semidirect |
| 26. C4×D212 | C22 | semidirect |
| 27. C2×C4⋊Dic53 | C22 | semidirect |
| 28. #13133151 | C22 | semidirect |
| 29. #13133151 | C22 | semidirect |
| 32. #13133139 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 35. #13133139 | C22 | semidirect |
| 36. C22×C8×C53 | C22 | semidirect |
| 38. C4⋊C8×C53 | C22 | semidirect |
| 39. C22⋊C8×C53 | C22 | semidirect |
| 40. C4×C8×C53 | C22 | semidirect |
| 85. D4×C53 | D8 | semidirect |
| 106. D212 | #41 | semidirect |
| 152. C8×D4 | D53 | semidirect |
| 154. C53 | #3294 | semidirect |
| 160. C22×C8 | C2×D53 | semidirect |
| 175. C4⋊C8 | C2×D53 | semidirect |
| 182. C22⋊C8 | C2×D53 | semidirect |
| 183. C4×C8 | C2×D53 | semidirect |
| 240. D4 | D424 | semidirect |