Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
536 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19145246 | C2 | semidirect |
| 2. #19143493 | C2 | semidirect |
| 3. #19136811 | C2 | semidirect |
| 4. #19136768 | C2 | semidirect |
| 5. #19136672 | C2 | semidirect |
| 6. #19136671 | C2 | semidirect |
| 7. #19136542 | C2 | semidirect |
| 8. #19136492 | C2 | semidirect |
| 9. #19136490 | C2 | semidirect |
| 10. #19136410 | C2 | semidirect |
| 11. C43×#2231 | C2 | semidirect |
| 17. #14583276 | C22 | semidirect |
| 26. #14583010 | C22 | semidirect |
| 31. #14582721 | C22 | semidirect |
| 32. #14582720 | C22 | semidirect |
| 33. #14582713 | C22 | semidirect |
| 34. #14582711 | C22 | semidirect |
| 37. #14582676 | C22 | semidirect |
| 38. C43×#499 | C22 | semidirect |
| 40. C43×#365 | C22 | semidirect |
| 41. C43×#364 | C22 | semidirect |
| 211. #2231 | D43 | semidirect |
| 229. #499 | C2×D43 | semidirect |
| 246. #365 | C2×D43 | semidirect |
| 248. #364 | C2×D43 | semidirect |
| 255. C43 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145246 | 2 |
| #19143493 | 2 |
| #19136811 | 2 |
| #19136768 | 2 |
| #19136672 | 2 |
| #19136671 | 2 |
| #19136542 | 2 |
| #19136492 | 2 |
| #19136490 | 2 |
| #19136410 | 2 |
| C43×#2231 | 2 |
| #33692 | 43 |