Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D43 | C2 | semidirect |
| 3. #19136838 | C2 | semidirect |
| 4. #19136837 | C2 | semidirect |
| 5. #19136836 | C2 | semidirect |
| 6. #19136835 | C2 | semidirect |
| 7. #357×D43 | C2 | semidirect |
| 8. #346×D43 | C2 | semidirect |
| 9. C43×#2244 | C2 | semidirect |
| 15. #14583301 | C22 | semidirect |
| 16. #14583300 | C22 | semidirect |
| 26. #14582701 | C22 | semidirect |
| 27. #14582700 | C22 | semidirect |
| 28. #14582699 | C22 | semidirect |
| 29. #14582675 | C22 | semidirect |
| 30. #14582674 | C22 | semidirect |
| 31. C43×#499 | C22 | semidirect |
| 33. C43×#357 | C22 | semidirect |
| 34. C43×#346 | C22 | semidirect |
| 157. #2244 | D43 | direct (N × H) |
| 164. D43 | #2244 | direct (N × H) |
| 174. #499 | C2×D43 | semidirect |
| 186. #357 | C2×D43 | semidirect |
| 189. #346 | C2×D43 | semidirect |
| 190. C43 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D43 | 2 |
| #493×D43 | 2 |
| #19136838 | 2 |
| #19136837 | 2 |
| #19136836 | 2 |
| #19136835 | 2 |
| #357×D43 | 2 |
| #346×D43 | 2 |
| C43×#2244 | 2 |
| C2×#2244 | 43 |