Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 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. #19145245 | C2 | semidirect |
| 2. #19143499 | C2 | semidirect |
| 3. #19136810 | C2 | semidirect |
| 4. #19136772 | C2 | semidirect |
| 5. #19136672 | C2 | semidirect |
| 6. #19136543 | C2 | semidirect |
| 7. #19136495 | C2 | semidirect |
| 8. C43×#2166 | C2 | semidirect |
| 13. #14583301 | C22 | semidirect |
| 14. #14583276 | C22 | semidirect |
| 22. #14583012 | C22 | semidirect |
| 26. #14582722 | C22 | semidirect |
| 27. #14582713 | C22 | semidirect |
| 30. C43×#364 | C22 | semidirect |
| 32. C43×#347 | C22 | semidirect |
| 169. #2166 | D43 | semidirect |
| 194. #364 | C2×D43 | semidirect |
| 198. #347 | C2×D43 | semidirect |
| 199. C43 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145245 | 2 |
| #19143499 | 2 |
| #19136810 | 2 |
| #19136772 | 2 |
| #19136672 | 2 |
| #19136543 | 2 |
| #19136495 | 2 |
| C43×#2166 | 2 |
| #33692 | 43 |