Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#13133205 | C2 | semidirect |
| 2. #16811005 | C2 | semidirect |
| 3. #16810980 | C2 | semidirect |
| 4. #16810845 | C2 | semidirect |
| 5. #16810838 | C2 | semidirect |
| 6. #16810778 | C2 | semidirect |
| 7. #16810773 | C2 | semidirect |
| 8. #16810761 | C2 | semidirect |
| 10. #16810676 | C2 | semidirect |
| 11. C53×#529 | C2 | semidirect |
| 14. C2×#11719925 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133140 | C22 | semidirect |
| 26. #13133140 | C22 | semidirect |
| 31. C4×#88322 | C22 | semidirect |
| 33. #125×C53 | C22 | semidirect |
| 34. #124×C53 | C22 | semidirect |
| 38. C4×Q8×C53 | C22 | semidirect |
| 40. C4×D4×C53 | C22 | semidirect |
| 144. #529 | D53 | semidirect |
| 155. C53 | #3211 | semidirect |
| 163. #125 | C2×D53 | semidirect |
| 168. #124 | C2×D53 | semidirect |
| 172. C4×Q8 | C2×D53 | semidirect |
| 174. C4×D4 | C2×D53 | semidirect |