Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
3936 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3936 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#14583061 | C2 | semidirect |
| 2. C2×#14583050 | C2 | semidirect |
| 3. #19140324 | C2 | semidirect |
| 4. #19134535 | C2 | semidirect |
| 5. #19134526 | C2 | semidirect |
| 6. #19134507 | C2 | semidirect |
| 8. C22×#10621885 | C22 | semidirect |
| 9. C22×#10621883 | C22 | semidirect |
| 10. C2×#13063304 | C22 | semidirect |
| 13. C2×#13063249 | C22 | semidirect |
| 14. C2×#13063246 | C22 | semidirect |
| 15. C2×#13063246 | C22 | semidirect |
| 16. C2×C22⋊(C43⋊C8) | C22 | semidirect |
| 17. C2×C22⋊(C43⋊C8) | C22 | semidirect |
| 20. #14582759 | C22 | semidirect |
| 218. C43 | #32886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583061 | 2 |
| C2×#14583050 | 2 |
| #19140324 | 2 |
| #19134535 | 2 |
| #19134526 | 2 |
| #19134507 | 2 |
| C22×H(5,𝔽2)×C43 | 2 |
| #32886 | 43 |