Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19145335 | C2 | semidirect |
| 3. #19136814 | C2 | semidirect |
| 4. #19136765 | C2 | semidirect |
| 5. #19136675 | C2 | semidirect |
| 8. #19136489 | C2 | semidirect |
| 9. #19136485 | C2 | semidirect |
| 10. #19136404 | C2 | semidirect |
| 11. C43×#2239 | C2 | semidirect |
| 17. #14583296 | C22 | semidirect |
| 18. #14583277 | C22 | semidirect |
| 26. #14583006 | C22 | semidirect |
| 27. #14583005 | C22 | semidirect |
| 31. #14582723 | C22 | semidirect |
| 32. #14582719 | C22 | semidirect |
| 33. #14582714 | C22 | semidirect |
| 37. #14582676 | C22 | semidirect |
| 40. C43×#365 | C22 | semidirect |
| 41. C43×#362 | C22 | semidirect |
| 194. #2239 | D43 | semidirect |
| 228. #365 | C2×D43 | semidirect |
| 231. #362 | C2×D43 | semidirect |
| 237. C43 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145335 | 2 |
| #19143504 | 2 |
| #19136814 | 2 |
| #19136765 | 2 |
| #19136675 | 2 |
| #19136548 | 2 |
| #19136545 | 2 |
| #19136489 | 2 |
| #19136485 | 2 |
| #19136404 | 2 |
| C43×#2239 | 2 |
| #33689 | 43 |