Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. #19145084 | C2 | semidirect |
| 3. #19143447 | C2 | semidirect |
| 4. #19136652 | C2 | semidirect |
| 5. #19136638 | C2 | semidirect |
| 6. #19136353 | C2 | semidirect |
| 7. #19136315 | C2 | semidirect |
| 8. #19136303 | C2 | semidirect |
| 9. C22×SD32×C43 | C2 | semidirect |
| 19. #14583284 | C22 | semidirect |
| 20. #14583277 | C22 | semidirect |
| 26. Dic43⋊C16 | C22 | semidirect |
| 27. #14582704 | C22 | semidirect |
| 28. #14582703 | C22 | semidirect |
| 29. #14582701 | C22 | semidirect |
| 173. C22×SD32 | D43 | semidirect |
| 211. C43 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583335 | 2 |
| #19145084 | 2 |
| #19143447 | 2 |
| #19136652 | 2 |
| #19136638 | 2 |
| #19136353 | 2 |
| #19136315 | 2 |
| #19136303 | 2 |
| C22×SD32×C43 | 2 |
| #33586 | 43 |