Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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×C4×D212 | C2 | semidirect |
| 2. #16810951 | C2 | semidirect |
| 3. #16810934 | C2 | semidirect |
| 4. #16810920 | C2 | semidirect |
| 5. #16810835 | C2 | semidirect |
| 6. #16810773 | C2 | semidirect |
| 8. #16810733 | C2 | semidirect |
| 9. #16810721 | C2 | semidirect |
| 10. #16810680 | C2 | semidirect |
| 11. C53×#529 | C2 | semidirect |
| 22. #13133150 | C22 | semidirect |
| 23. #13133148 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133141 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 31. #13133128 | C22 | semidirect |
| 33. #125×C53 | C22 | semidirect |
| 34. #124×C53 | C22 | semidirect |
| 38. C4×Q8×C53 | C22 | semidirect |
| 40. C4×D4×C53 | C22 | semidirect |
| 141. #529 | D53 | semidirect |
| 152. C53 | #3114 | semidirect |
| 158. #125 | C2×D53 | semidirect |
| 159. #124 | C2×D53 | semidirect |
| 163. C4×Q8 | C2×D53 | semidirect |
| 169. C4×D4 | C2×D53 | semidirect |