Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 179 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. #19145510 | C2 | semidirect |
| 2. #19145048 | C2 | semidirect |
| 3. #19133678 | C2 | semidirect |
| 4. #19133649 | C2 | semidirect |
| 5. #19133257 | C2 | semidirect |
| 6. #19133012 | C2 | semidirect |
| 7. C43×#3549 | C2 | semidirect |
| 9. C2×#13063322 | C22 | semidirect |
| 13. #14583273 | C22 | semidirect |
| 15. #14583094 | C22 | semidirect |
| 17. #14582952 | C22 | semidirect |
| 18. C4×#10621877 | C22 | semidirect |
| 19. #14582648 | C22 | semidirect |
| 20. #14582643 | C22 | semidirect |
| 21. D4⋊(C43⋊C8) | C22 | semidirect |
| 24. C43×#555 | C22 | semidirect |
| 26. D42×C43 | C22 | semidirect |
| 174. #3549 | D43 | semidirect |
| 190. #555 | C2×D43 | semidirect |
| 192. D42 | C2×D43 | semidirect |
| 210. C43 | #18714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145510 | 2 |
| #19145048 | 2 |
| #19133678 | 2 |
| #19133649 | 2 |
| #19133257 | 2 |
| #19133012 | 2 |
| C43×#3549 | 2 |
| #18714 | 43 |