Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 171 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. #19145598 | C2 | semidirect |
| 2. #19144981 | C2 | semidirect |
| 3. #19133901 | C2 | semidirect |
| 4. #19133219 | C2 | semidirect |
| 5. #19133193 | C2 | semidirect |
| 7. #14583456 | C22 | semidirect |
| 8. #14583294 | C22 | semidirect |
| 9. #14583258 | C22 | semidirect |
| 10. #14583258 | C22 | semidirect |
| 15. #14582956 | C22 | semidirect |
| 18. C4×#10621877 | C22 | semidirect |
| 19. #14582639 | C22 | semidirect |
| 20. #14582639 | C22 | semidirect |
| 33. #13063325 | C23 | semidirect |
| 44. #13063236 | C23 | semidirect |
| 45. #13063236 | C23 | semidirect |
| 212. C43 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145598 | 2 |
| #19144981 | 2 |
| #19133901 | 2 |
| #19133219 | 2 |
| #19133193 | 2 |
| C2×C43×H(3,𝔽4) | 2 |
| #18997 | 43 |