Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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×#14583334 | C2 | semidirect |
| 2. C22×D688 | C2 | semidirect |
| 3. #19145082 | C2 | semidirect |
| 4. #19143446 | C2 | semidirect |
| 5. #19136653 | C2 | semidirect |
| 6. #19136629 | C2 | semidirect |
| 7. #19136353 | C2 | semidirect |
| 8. #19136310 | C2 | semidirect |
| 9. C43×#2138 | C2 | semidirect |
| 16. C2×#13063268 | C22 | semidirect |
| 19. C2×#13063266 | C22 | semidirect |
| 22. #14583284 | C22 | semidirect |
| 23. #14583274 | C22 | semidirect |
| 25. #14582981 | C22 | semidirect |
| 28. Dic43⋊C16 | C22 | semidirect |
| 29. #14582699 | C22 | semidirect |
| 33. C43×#358 | C22 | semidirect |
| 34. C43×#357 | C22 | semidirect |
| 44. C2×D344 | D4 | semidirect |
| 184. #2138 | D43 | semidirect |
| 213. #358 | C2×D43 | semidirect |
| 215. #357 | C2×D43 | semidirect |
| 216. C43 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583334 | 2 |
| C22×D688 | 2 |
| #19145082 | 2 |
| #19143446 | 2 |
| #19136653 | 2 |
| #19136629 | 2 |
| #19136353 | 2 |
| #19136310 | 2 |
| C43×#2138 | 2 |
| #33585 | 43 |