Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 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×#14583335 | C2 | semidirect |
| 2. #19145076 | C2 | semidirect |
| 3. #19143447 | C2 | semidirect |
| 4. #19136648 | C2 | semidirect |
| 5. #19136628 | C2 | semidirect |
| 6. #19136353 | C2 | semidirect |
| 7. #19136311 | C2 | semidirect |
| 8. #19136303 | C2 | semidirect |
| 9. C22×D16×C43 | C2 | semidirect |
| 15. C2×#13063269 | C22 | semidirect |
| 16. C2×#13063266 | C22 | semidirect |
| 19. #14583282 | C22 | semidirect |
| 20. #14583274 | C22 | semidirect |
| 22. D8×Dic43 | C22 | semidirect |
| 26. Dic43⋊C16 | C22 | semidirect |
| 27. #14582704 | C22 | semidirect |
| 28. #14582701 | C22 | semidirect |
| 29. #14582700 | C22 | semidirect |
| 70. C2×D8×C43 | D4 | semidirect |
| 177. C22×D16 | D43 | semidirect |
| 216. C43 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583335 | 2 |
| #19145076 | 2 |
| #19143447 | 2 |
| #19136648 | 2 |
| #19136628 | 2 |
| #19136353 | 2 |
| #19136311 | 2 |
| #19136303 | 2 |
| C22×D16×C43 | 2 |
| #33585 | 43 |