Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 2. #19132899 | C2 | semidirect |
| 3. #19132897 | C2 | semidirect |
| 4. #19132896 | C2 | semidirect |
| 5. #19132895 | C2 | semidirect |
| 6. #19132894 | C2 | semidirect |
| 7. C43×#1454 | C2 | semidirect |
| 18. #14582621 | C22 | semidirect |
| 19. #14582621 | C22 | semidirect |
| 20. #14582620 | C22 | semidirect |
| 21. C8×C43⋊C8 | C22 | semidirect |
| 23. C43×#322 | C22 | semidirect |
| 24. C82×C43 | C22 | semidirect |
| 101. #1454 | D43 | semidirect |
| 120. #322 | C2×D43 | semidirect |
| 122. C82 | C2×D43 | semidirect |
| 123. C43 | #17339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143223 | 2 |
| #19132899 | 2 |
| #19132897 | 2 |
| #19132896 | 2 |
| #19132895 | 2 |
| #19132894 | 2 |
| C43×#1454 | 2 |
| #17339 | 43 |