Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
778 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 143 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. #19146407 | C2 | semidirect |
| 2. #19146194 | C2 | semidirect |
| 3. #19134057 | C2 | semidirect |
| 4. #19134029 | C2 | semidirect |
| 5. #19133827 | C2 | semidirect |
| 6. #19133647 | C2 | semidirect |
| 7. #19133481 | C2 | semidirect |
| 8. C8×D344 | C2 | semidirect |
| 9. C43×#1706 | C2 | semidirect |
| 12. #14583534 | C22 | semidirect |
| 14. #14583176 | C22 | semidirect |
| 17. #14583101 | C22 | semidirect |
| 25. #14582978 | C22 | semidirect |
| 26. C8×D172 | C22 | semidirect |
| 28. #14582652 | C22 | semidirect |
| 29. #14582652 | C22 | semidirect |
| 30. #14582645 | C22 | semidirect |
| 31. #14582643 | C22 | semidirect |
| 32. #14582628 | C22 | semidirect |
| 33. #14582628 | C22 | semidirect |
| 34. C43×#500 | C22 | semidirect |
| 36. C43×#492 | C22 | semidirect |
| 37. C43×#486 | C22 | semidirect |
| 38. C82×C43 | C22 | semidirect |
| 126. D344 | D8 | semidirect |
| 189. #1706 | D43 | semidirect |
| 205. #500 | C2×D43 | semidirect |
| 207. #492 | C2×D43 | semidirect |
| 208. #486 | C2×D43 | semidirect |
| 230. C82 | C2×D43 | semidirect |
| 231. C43 | #19884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146407 | 2 |
| #19146194 | 2 |
| #19134057 | 2 |
| #19134029 | 2 |
| #19133827 | 2 |
| #19133647 | 2 |
| #19133481 | 2 |
| C8×D344 | 2 |
| C43×#1706 | 2 |
| #19884 | 43 |