Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13133240 | C2 | semidirect |
| 2. C22×C8×D53 | C2 | semidirect |
| 3. #16811136 | C2 | semidirect |
| 4. #16810861 | C2 | semidirect |
| 5. #16810860 | C2 | semidirect |
| 6. #16810859 | C2 | semidirect |
| 7. #16810855 | C2 | semidirect |
| 8. #16810854 | C2 | semidirect |
| 9. #16810660 | C2 | semidirect |
| 10. #16810618 | C2 | semidirect |
| 11. C53×#467 | C2 | semidirect |
| 15. C2×#11719924 | C22 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 31. #13133151 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133141 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 35. #13133137 | C22 | semidirect |
| 36. C2×Q16×C53 | C22 | semidirect |
| 39. #107×C53 | C22 | semidirect |
| 40. #103×C53 | C22 | semidirect |
| 80. C8×D53 | D4 | semidirect |
| 118. C22×C53 | #135 | semidirect |
| 129. C2×D53 | #135 | semidirect |
| 150. #467 | D53 | semidirect |
| 157. C53 | #3050 | semidirect |
| 161. C2×Q16 | C2×D53 | semidirect |
| 181. #107 | C2×D53 | semidirect |
| 184. #103 | C2×D53 | semidirect |
| 274. C22 | #13133240 | semidirect |