Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16811133 | C2 | semidirect |
| 2. C2×#13133188 | C2 | semidirect |
| 3. #16810959 | C2 | semidirect |
| 4. #16810945 | C2 | semidirect |
| 5. #16810939 | C2 | semidirect |
| 6. #16810856 | C2 | semidirect |
| 7. #16810851 | C2 | semidirect |
| 8. #16810774 | C2 | semidirect |
| 9. #16810765 | C2 | semidirect |
| 10. C22⋊C8×D53 | C2 | semidirect |
| 11. C53×#447 | C2 | semidirect |
| 12. C2×#11719947 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 16. C2×C8×D53 | C22 | semidirect |
| 18. #13133197 | C22 | semidirect |
| 24. #13133188 | C22 | semidirect |
| 28. #13133175 | C22 | semidirect |
| 31. #13133151 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133138 | C22 | semidirect |
| 35. #13133138 | C22 | semidirect |
| 37. #13133129 | C22 | semidirect |
| 39. C2×D8×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 168. #447 | D53 | semidirect |
| 170. C53 | #3188 | semidirect |
| 176. C2×D8 | C2×D53 | semidirect |
| 198. #102 | C2×D53 | semidirect |