Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
564 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19145328 | C2 | semidirect |
| 2. #19143505 | C2 | semidirect |
| 3. #19136810 | C2 | semidirect |
| 4. #19136807 | C2 | semidirect |
| 5. #19136764 | C2 | semidirect |
| 6. #19136669 | C2 | semidirect |
| 7. #19136541 | C2 | semidirect |
| 8. #19136494 | C2 | semidirect |
| 9. #19136490 | C2 | semidirect |
| 10. #19136404 | C2 | semidirect |
| 11. C43×#2190 | C2 | semidirect |
| 15. #14583296 | C22 | semidirect |
| 16. #14583274 | C22 | semidirect |
| 24. #14583011 | C22 | semidirect |
| 25. #14583010 | C22 | semidirect |
| 30. #14582722 | C22 | semidirect |
| 31. #14582721 | C22 | semidirect |
| 32. #14582719 | C22 | semidirect |
| 33. #14582713 | C22 | semidirect |
| 34. #14582712 | C22 | semidirect |
| 37. #14582676 | C22 | semidirect |
| 111. Q16×C43 | #41 | semidirect |
| 116. D8×C43 | #41 | semidirect |
| 209. #2190 | D43 | semidirect |
| 250. C43 | #33688 | semidirect |
| 319. Q16 | #10621900 | semidirect |
| 326. D8 | #10621900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145328 | 2 |
| #19143505 | 2 |
| #19136810 | 2 |
| #19136807 | 2 |
| #19136764 | 2 |
| #19136669 | 2 |
| #19136541 | 2 |
| #19136494 | 2 |
| #19136490 | 2 |
| #19136404 | 2 |
| C43×#2190 | 2 |
| #33688 | 43 |