Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 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. #19143506 | C2 | semidirect |
| 2. #19136807 | C2 | semidirect |
| 3. #19136763 | C2 | semidirect |
| 4. #19136668 | C2 | semidirect |
| 5. #19136540 | C2 | semidirect |
| 6. #19136491 | C2 | semidirect |
| 7. #19136407 | C2 | semidirect |
| 8. C43×#3184 | C2 | semidirect |
| 18. #14582721 | C22 | semidirect |
| 19. #14582720 | C22 | semidirect |
| 20. #14582712 | C22 | semidirect |
| 23. #14582677 | C22 | semidirect |
| 25. C43×#498 | C22 | semidirect |
| 26. C43×#493 | C22 | semidirect |
| 31. C43×#442 | C22 | semidirect |
| 107. Dic172 | #41 | semidirect |
| 109. D344 | #41 | semidirect |
| 165. #3184 | D43 | semidirect |
| 182. #498 | C2×D43 | semidirect |
| 183. #493 | C2×D43 | semidirect |
| 192. #442 | C2×D43 | semidirect |
| 202. C43 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143506 | 2 |
| #19136807 | 2 |
| #19136763 | 2 |
| #19136668 | 2 |
| #19136540 | 2 |
| #19136491 | 2 |
| #19136407 | 2 |
| C43×#3184 | 2 |
| #33688 | 43 |