Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133264 | C2 | semidirect |
| 2. C22×#11719923 | C2 | semidirect |
| 3. #16811190 | C2 | semidirect |
| 4. #16810765 | C2 | semidirect |
| 5. #16810760 | C2 | semidirect |
| 6. #16810633 | C2 | semidirect |
| 7. #16810619 | C2 | semidirect |
| 8. #16810591 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 15. C2×#11719947 | C22 | semidirect |
| 18. C2×Q8×D53 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 28. #13133141 | C22 | semidirect |
| 29. #13133138 | C22 | semidirect |
| 30. #13133129 | C22 | semidirect |
| 39. #41×C53 | D4 | semidirect |
| 70. C2×Dic106 | D4 | semidirect |
| 147. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 155. C53 | #3010 | semidirect |
| 191. #41 | C22⋊D53 | semidirect |