Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
982 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 199 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. #494×D43 | C2 | semidirect |
| 3. #486×D43 | C2 | semidirect |
| 4. #19134202 | C2 | semidirect |
| 5. #19134201 | C2 | semidirect |
| 6. #19134200 | C2 | semidirect |
| 7. #19134199 | C2 | semidirect |
| 8. C82×D43 | C2 | semidirect |
| 9. C43×#1709 | C2 | semidirect |
| 14. #14583279 | C22 | semidirect |
| 15. #14583278 | C22 | semidirect |
| 20. #14583247 | C22 | semidirect |
| 21. #14583246 | C22 | semidirect |
| 22. #14583245 | C22 | semidirect |
| 27. C8×C43⋊C8 | C22 | semidirect |
| 28. C8×C43⋊C8 | C22 | semidirect |
| 29. C43×#494 | C22 | semidirect |
| 31. C43×#486 | C22 | semidirect |
| 32. C82×C43 | C22 | semidirect |
| 149. #1709 | D43 | direct (N × H) |
| 155. D43 | #1709 | direct (N × H) |
| 163. #494 | C2×D43 | semidirect |
| 172. #486 | C2×D43 | semidirect |
| 178. C82 | C2×D43 | semidirect |
| 179. C43 | C2×#1709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #494×D43 | 2 |
| #493×D43 | 2 |
| #486×D43 | 2 |
| #19134202 | 2 |
| #19134201 | 2 |
| #19134200 | 2 |
| #19134199 | 2 |
| C82×D43 | 2 |
| C43×#1709 | 2 |
| C2×#1709 | 43 |