Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
580 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 91 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. #19143634 | C2 | semidirect |
| 3. C4×#13063239 | C2 | semidirect |
| 4. #19133111 | C2 | semidirect |
| 5. #19132449 | C2 | semidirect |
| 6. #19132448 | C2 | semidirect |
| 7. C43×#1507 | C2 | semidirect |
| 15. #14582837 | C4 | semidirect |
| 16. #14582834 | C4 | semidirect |
| 18. #14582813 | C4 | semidirect |
| 20. #14582807 | C4 | semidirect |
| 55. C22⋊(C43⋊C8) | D4 | semidirect |
| 77. C22⋊C8×C43 | D4 | semidirect |
| 247. #1507 | D43 | semidirect |
| 282. C43 | #9186 | semidirect |
| 322. C22⋊C8 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143634 | 2 |
| #19140480 | 2 |
| C4×#13063239 | 2 |
| #19133111 | 2 |
| #19132449 | 2 |
| #19132448 | 2 |
| C43×#1507 | 2 |
| #9186 | 43 |