Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 536 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. #19145240 | C2 | semidirect |
| 2. #19143497 | C2 | semidirect |
| 3. #19136809 | C2 | semidirect |
| 4. #19136770 | C2 | semidirect |
| 5. #19136670 | C2 | semidirect |
| 6. #19136543 | C2 | semidirect |
| 7. #19136540 | C2 | semidirect |
| 8. #19136496 | C2 | semidirect |
| 9. #19136492 | C2 | semidirect |
| 10. #19136408 | C2 | semidirect |
| 11. C43×#2238 | C2 | semidirect |
| 17. #14583299 | C22 | semidirect |
| 18. #14583274 | C22 | semidirect |
| 26. #14583011 | C22 | semidirect |
| 27. #14583010 | C22 | semidirect |
| 31. #14582723 | C22 | semidirect |
| 32. #14582719 | C22 | semidirect |
| 33. #14582711 | C22 | semidirect |
| 37. #14582676 | C22 | semidirect |
| 40. C43×#365 | C22 | semidirect |
| 41. C43×#361 | C22 | semidirect |
| 207. #2238 | D43 | semidirect |
| 243. #365 | C2×D43 | semidirect |
| 246. #361 | C2×D43 | semidirect |
| 252. C43 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145240 | 2 |
| #19143497 | 2 |
| #19136809 | 2 |
| #19136770 | 2 |
| #19136670 | 2 |
| #19136543 | 2 |
| #19136540 | 2 |
| #19136496 | 2 |
| #19136492 | 2 |
| #19136408 | 2 |
| C43×#2238 | 2 |
| #33692 | 43 |