Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #19145254 | C2 | semidirect |
| 3. #19136815 | C2 | semidirect |
| 4. #19136772 | C2 | semidirect |
| 5. #19136677 | C2 | semidirect |
| 7. #19136488 | C2 | semidirect |
| 8. C43×#2166 | C2 | semidirect |
| 13. #14583301 | C22 | semidirect |
| 14. #14583279 | C22 | semidirect |
| 22. #14583007 | C22 | semidirect |
| 26. #14582722 | C22 | semidirect |
| 27. #14582716 | C22 | semidirect |
| 30. C43×#364 | C22 | semidirect |
| 32. C43×#347 | C22 | semidirect |
| 164. #2166 | D43 | semidirect |
| 188. #364 | C2×D43 | semidirect |
| 192. #347 | C2×D43 | semidirect |
| 193. C43 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145254 | 2 |
| #19143499 | 2 |
| #19136815 | 2 |
| #19136772 | 2 |
| #19136677 | 2 |
| #19136548 | 2 |
| #19136488 | 2 |
| C43×#2166 | 2 |
| #33693 | 43 |