Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 1. C2×#14583340 | C2 | semidirect |
| 3. #19143463 | C2 | semidirect |
| 4. #19136655 | C2 | semidirect |
| 5. #19136633 | C2 | semidirect |
| 6. #19136353 | C2 | semidirect |
| 7. #19136311 | C2 | semidirect |
| 8. #19136303 | C2 | semidirect |
| 9. C22×SD32×C43 | C2 | semidirect |
| 15. C2×#13063271 | C22 | semidirect |
| 16. C2×#13063268 | C22 | semidirect |
| 22. Q16×Dic43 | C22 | semidirect |
| 26. Dic43⋊C16 | C22 | semidirect |
| 27. #14582704 | C22 | semidirect |
| 28. #14582701 | C22 | semidirect |
| 67. C2×Q16×C43 | D4 | semidirect |
| 173. C22×SD32 | D43 | semidirect |
| 211. C43 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583340 | 2 |
| #19145076 | 2 |
| #19143463 | 2 |
| #19136655 | 2 |
| #19136633 | 2 |
| #19136353 | 2 |
| #19136311 | 2 |
| #19136303 | 2 |
| C22×SD32×C43 | 2 |
| #33587 | 43 |