Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×D8×D53 | C2 | semidirect |
| 2. C2×#13133223 | C2 | semidirect |
| 3. #16811189 | C2 | semidirect |
| 4. #16810875 | C2 | semidirect |
| 5. #16810874 | C2 | semidirect |
| 6. #16810860 | C2 | semidirect |
| 7. #16810859 | C2 | semidirect |
| 8. #16810856 | C2 | semidirect |
| 9. #16810660 | C2 | semidirect |
| 10. #16810626 | C2 | semidirect |
| 11. C53×#466 | C2 | semidirect |
| 18. C2×#11719917 | C22 | semidirect |
| 20. C2×#11719912 | C22 | semidirect |
| 22. C2×C8×D53 | C22 | semidirect |
| 25. #13133192 | C22 | semidirect |
| 26. #13133191 | C22 | semidirect |
| 27. #13133188 | C22 | semidirect |
| 31. #13133151 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133138 | C22 | semidirect |
| 35. #13133137 | C22 | semidirect |
| 37. C22×C8×C53 | C22 | semidirect |
| 38. #121×C53 | C22 | semidirect |
| 39. #107×C53 | C22 | semidirect |
| 40. #102×C53 | C22 | semidirect |
| 80. C8×D53 | D4 | semidirect |
| 159. #466 | D53 | semidirect |
| 162. C53 | #3058 | semidirect |
| 175. C22×C8 | C2×D53 | semidirect |
| 181. #121 | C2×D53 | semidirect |
| 186. #107 | C2×D53 | semidirect |
| 191. #102 | C2×D53 | semidirect |