Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13133243 | C2 | semidirect |
| 2. #16811190 | C2 | semidirect |
| 3. #16811098 | C2 | semidirect |
| 4. #16810836 | C2 | semidirect |
| 5. #16810816 | C2 | semidirect |
| 6. #16810649 | C2 | semidirect |
| 7. #16810628 | C2 | semidirect |
| 8. #16810620 | C2 | semidirect |
| 9. C22×D8×C53 | C2 | semidirect |
| 12. C2×#11719923 | C22 | semidirect |
| 13. C2×#11719922 | C22 | semidirect |
| 15. #13133213 | C22 | semidirect |
| 16. #13133204 | C22 | semidirect |
| 20. D4×Dic53 | C22 | semidirect |
| 24. #13133146 | C22 | semidirect |
| 25. #13133142 | C22 | semidirect |
| 26. #13133139 | C22 | semidirect |
| 27. #13133138 | C22 | semidirect |
| 40. C2×D4×C53 | D4 | semidirect |
| 123. C22×D8 | D53 | semidirect |
| 131. C53 | #3041 | semidirect |
| 168. C2×D4 | C22⋊D53 | semidirect |