Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #19147736 | C2 | semidirect |
| 2. #19146395 | C2 | semidirect |
| 3. #19136845 | C2 | semidirect |
| 4. #19136715 | C2 | semidirect |
| 5. #19136672 | C2 | semidirect |
| 6. #19136554 | C2 | semidirect |
| 7. #19136477 | C2 | semidirect |
| 8. C43×#2170 | C2 | semidirect |
| 9. #14583704 | C22 | semidirect |
| 12. #14583337 | C22 | semidirect |
| 16. C2×D688 | C22 | semidirect |
| 17. C2×D688 | C22 | semidirect |
| 18. #14583276 | C22 | semidirect |
| 20. #14583169 | C22 | semidirect |
| 22. #14583017 | C22 | semidirect |
| 23. #14582729 | C22 | semidirect |
| 24. #14582713 | C22 | semidirect |
| 25. #14582707 | C22 | semidirect |
| 26. C43×#504 | C22 | semidirect |
| 28. C43×#364 | C22 | semidirect |
| 29. C43×#350 | C22 | semidirect |
| 30. C4×C16×C43 | C22 | semidirect |
| 45. Dic344 | D4 | semidirect |
| 47. #13063270 | D4 | semidirect |
| 52. D688 | D4 | semidirect |
| 145. #2170 | D43 | semidirect |
| 160. #504 | C2×D43 | semidirect |
| 168. #364 | C2×D43 | semidirect |
| 171. #350 | C2×D43 | semidirect |
| 172. C4×C16 | C2×D43 | semidirect |
| 173. C43 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147736 | 2 |
| #19146395 | 2 |
| #19136845 | 2 |
| #19136715 | 2 |
| #19136672 | 2 |
| #19136554 | 2 |
| #19136477 | 2 |
| C43×#2170 | 2 |
| #33858 | 43 |