Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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×D424 | C2 | semidirect |
| 3. #16811264 | C2 | semidirect |
| 4. #16811008 | C2 | semidirect |
| 5. #16810860 | C2 | semidirect |
| 6. #16810841 | C2 | semidirect |
| 7. #16810773 | C2 | semidirect |
| 8. #16810771 | C2 | semidirect |
| 9. #16810705 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C53×#467 | C2 | semidirect |
| 12. C2×#11719949 | C22 | semidirect |
| 15. C2×#11719924 | C22 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 21. C2×C8×D53 | C22 | semidirect |
| 22. #13133206 | C22 | semidirect |
| 25. #13133192 | C22 | semidirect |
| 27. #13133179 | C22 | semidirect |
| 30. #13133146 | C22 | semidirect |
| 31. #13133137 | C22 | semidirect |
| 32. #13133137 | C22 | semidirect |
| 34. #13133129 | C22 | semidirect |
| 35. C8×Dic53 | C22 | semidirect |
| 36. C2×Q16×C53 | C22 | semidirect |
| 39. #107×C53 | C22 | semidirect |
| 40. #103×C53 | C22 | semidirect |
| 78. D424 | D4 | semidirect |
| 116. C22×C53 | #135 | semidirect |
| 148. #467 | D53 | semidirect |
| 155. C53 | #3280 | semidirect |
| 159. C2×Q16 | C2×D53 | semidirect |
| 177. #107 | C2×D53 | semidirect |
| 179. #103 | C2×D53 | semidirect |
| 270. C22 | #13133240 | semidirect |