Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 472 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. #19147733 | C2 | semidirect |
| 2. #19136909 | C2 | semidirect |
| 3. #19136907 | C2 | semidirect |
| 4. #19136905 | C2 | semidirect |
| 5. C2×D1376 | C2 | semidirect |
| 6. D32×D43 | C2 | semidirect |
| 7. #19136888 | C2 | semidirect |
| 8. C43×#2262 | C2 | semidirect |
| 12. #14583332 | C22 | semidirect |
| 13. C2×D688 | C22 | semidirect |
| 14. D16×D43 | C22 | semidirect |
| 16. #14582736 | C22 | semidirect |
| 17. D1376 | C22 | semidirect |
| 18. D1376 | C22 | semidirect |
| 19. #14582734 | C22 | semidirect |
| 20. #14582733 | C22 | semidirect |
| 21. #14582732 | C22 | semidirect |
| 22. C32×D43 | C22 | semidirect |
| 23. C43×#508 | C22 | semidirect |
| 24. C43×Q64 | C22 | semidirect |
| 25. C43×SD64 | C22 | semidirect |
| 26. C43×D32 | C22 | semidirect |
| 27. C2×C32×C43 | C22 | semidirect |
| 106. #2262 | D43 | semidirect |
| 119. #508 | C2×D43 | semidirect |
| 123. Q64 | C2×D43 | semidirect |
| 125. SD64 | C2×D43 | semidirect |
| 129. D32 | C2×D43 | semidirect |
| 133. C2×C32 | C2×D43 | semidirect |
| 134. C43 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147733 | 2 |
| #19136909 | 2 |
| #19136907 | 2 |
| #19136905 | 2 |
| C2×D1376 | 2 |
| D32×D43 | 2 |
| #19136888 | 2 |
| C43×#2262 | 2 |
| #33982 | 43 |