Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 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. #508×D43 | C2 | semidirect |
| 2. #19136914 | C2 | semidirect |
| 3. #19136911 | C2 | semidirect |
| 4. #19136909 | C2 | semidirect |
| 5. #19136906 | C2 | semidirect |
| 6. #19136904 | C2 | semidirect |
| 7. #19136902 | C2 | semidirect |
| 8. C2×#14582732 | C2 | semidirect |
| 9. C43×#2262 | C2 | semidirect |
| 12. #14583331 | C22 | semidirect |
| 16. Q32×D43 | C22 | semidirect |
| 18. D16×D43 | C22 | semidirect |
| 20. Dic688 | C22 | semidirect |
| 21. #14582739 | C22 | semidirect |
| 22. #14582738 | C22 | semidirect |
| 23. #14582737 | C22 | semidirect |
| 24. #14582736 | C22 | semidirect |
| 25. D1376 | C22 | semidirect |
| 26. #14582734 | C22 | semidirect |
| 27. #14582732 | C22 | semidirect |
| 28. #14582732 | C22 | semidirect |
| 29. C2×C43⋊C32 | C22 | semidirect |
| 30. C43×#508 | C22 | semidirect |
| 31. C43×Q64 | C22 | semidirect |
| 32. C43×SD64 | C22 | semidirect |
| 33. C43×D32 | C22 | semidirect |
| 34. C2×C32×C43 | C22 | semidirect |
| 134. #2262 | D43 | semidirect |
| 147. #508 | C2×D43 | semidirect |
| 154. Q64 | C2×D43 | semidirect |
| 158. SD64 | C2×D43 | semidirect |
| 161. D32 | C2×D43 | semidirect |
| 165. C2×C32 | C2×D43 | semidirect |
| 166. C43 | #33981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D43 | 2 |
| #19136914 | 2 |
| #19136911 | 2 |
| #19136909 | 2 |
| #19136906 | 2 |
| #19136904 | 2 |
| #19136902 | 2 |
| C2×#14582732 | 2 |
| C43×#2262 | 2 |
| #33981 | 43 |