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. #19147732 | C2 | semidirect |
| 2. #19136908 | C2 | semidirect |
| 3. #19136906 | C2 | semidirect |
| 4. #19136904 | C2 | semidirect |
| 5. #19136901 | C2 | semidirect |
| 6. D32×D43 | C2 | semidirect |
| 7. #19136888 | C2 | semidirect |
| 8. C2×C43×D32 | C2 | semidirect |
| 12. #14583331 | C22 | semidirect |
| 13. #14583328 | C22 | semidirect |
| 14. D16×D43 | C22 | semidirect |
| 16. Dic688 | C22 | semidirect |
| 17. #14582738 | C22 | semidirect |
| 18. #14582737 | C22 | semidirect |
| 19. D1376 | C22 | semidirect |
| 20. #14582734 | C22 | semidirect |
| 21. #14582733 | C22 | semidirect |
| 22. #14582732 | C22 | semidirect |
| 23. C32×D43 | C22 | semidirect |
| 24. C2×D16×C43 | C22 | semidirect |
| 25. C43×D32 | C22 | semidirect |
| 26. C43×D32 | C22 | semidirect |
| 27. C2×C32×C43 | C22 | semidirect |
| 108. C2×D32 | D43 | semidirect |
| 121. C2×D16 | C2×D43 | semidirect |
| 128. D32 | 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 |
|---|---|
| #19147732 | 2 |
| #19136908 | 2 |
| #19136906 | 2 |
| #19136904 | 2 |
| #19136901 | 2 |
| D32×D43 | 2 |
| #19136888 | 2 |
| C2×C43×D32 | 2 |
| #33982 | 43 |