Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 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. #19145336 | C2 | semidirect |
| 4. #19134258 | C2 | semidirect |
| 5. #19134253 | C2 | semidirect |
| 6. #19134252 | C2 | semidirect |
| 7. #19134208 | C2 | semidirect |
| 8. #19132898 | C2 | semidirect |
| 9. C43×#3185 | C2 | semidirect |
| 12. #14583295 | C22 | semidirect |
| 13. #14583278 | C22 | semidirect |
| 16. #14583251 | C22 | semidirect |
| 17. #14583249 | C22 | semidirect |
| 29. #14582621 | C22 | semidirect |
| 30. #14582620 | C22 | semidirect |
| 31. C8×C43⋊C8 | C22 | semidirect |
| 33. C43×#498 | C22 | semidirect |
| 34. C43×#494 | C22 | semidirect |
| 35. C43×#487 | C22 | semidirect |
| 157. #3185 | D43 | semidirect |
| 173. #498 | C2×D43 | semidirect |
| 175. #494 | C2×D43 | semidirect |
| 180. #487 | C2×D43 | semidirect |
| 198. C43 | #19753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145336 | 2 |
| #19144971 | 2 |
| #19144970 | 2 |
| #19134258 | 2 |
| #19134253 | 2 |
| #19134252 | 2 |
| #19134208 | 2 |
| #19132898 | 2 |
| C43×#3185 | 2 |
| #19753 | 43 |