Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19145338 | C2 | semidirect |
| 3. #19136813 | C2 | semidirect |
| 4. #19136767 | C2 | semidirect |
| 5. #19136766 | C2 | semidirect |
| 6. #19136673 | C2 | semidirect |
| 8. #19136489 | C2 | semidirect |
| 9. #19136487 | C2 | semidirect |
| 10. #19136406 | C2 | semidirect |
| 11. C43×#2214 | C2 | semidirect |
| 16. #14583297 | C22 | semidirect |
| 26. #14583006 | C22 | semidirect |
| 30. #14582723 | C22 | semidirect |
| 31. #14582722 | C22 | semidirect |
| 32. #14582720 | C22 | semidirect |
| 33. #14582715 | C22 | semidirect |
| 37. #14582676 | C22 | semidirect |
| 39. C43×#494 | C22 | semidirect |
| 41. C43×#364 | C22 | semidirect |
| 42. C43×#362 | C22 | semidirect |
| 214. #2214 | D43 | semidirect |
| 230. #494 | C2×D43 | semidirect |
| 248. #364 | C2×D43 | semidirect |
| 250. #362 | C2×D43 | semidirect |
| 255. C43 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145338 | 2 |
| #19143500 | 2 |
| #19136813 | 2 |
| #19136767 | 2 |
| #19136766 | 2 |
| #19136673 | 2 |
| #19136544 | 2 |
| #19136489 | 2 |
| #19136487 | 2 |
| #19136406 | 2 |
| C43×#2214 | 2 |
| #33689 | 43 |