Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 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. #19136908 | C2 | semidirect |
| 3. #19136907 | C2 | semidirect |
| 4. #19136902 | C2 | semidirect |
| 5. C2×#14582734 | C2 | semidirect |
| 6. #19136889 | C2 | semidirect |
| 7. C43×#3415 | C2 | semidirect |
| 10. #14583331 | C22 | semidirect |
| 11. C2×D688 | C22 | semidirect |
| 12. #14582739 | C22 | semidirect |
| 13. #14582737 | C22 | semidirect |
| 14. #14582736 | C22 | semidirect |
| 15. #14582734 | C22 | semidirect |
| 16. #14582734 | C22 | semidirect |
| 17. #14582733 | C22 | semidirect |
| 18. C2×C43⋊C32 | C22 | semidirect |
| 21. C43×#508 | C22 | semidirect |
| 22. C2×D16×C43 | C22 | semidirect |
| 94. #3415 | D43 | semidirect |
| 109. #508 | C2×D43 | semidirect |
| 111. C2×D16 | C2×D43 | semidirect |
| 120. C43 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147736 | 2 |
| #19136908 | 2 |
| #19136907 | 2 |
| #19136902 | 2 |
| C2×#14582734 | 2 |
| #19136889 | 2 |
| C43×#3415 | 2 |
| #33982 | 43 |