Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 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. #19147733 | C2 | semidirect |
| 2. #19146395 | C2 | semidirect |
| 3. #19136845 | C2 | semidirect |
| 4. #19136716 | C2 | semidirect |
| 5. #19136671 | C2 | semidirect |
| 6. #19136553 | C2 | semidirect |
| 7. #19136433 | C2 | semidirect |
| 8. C43×#2178 | C2 | semidirect |
| 10. #14583701 | C22 | semidirect |
| 12. #14583334 | C22 | semidirect |
| 14. C2×D688 | C22 | semidirect |
| 15. C2×D688 | C22 | semidirect |
| 17. #14583315 | C22 | semidirect |
| 18. #14583276 | C22 | semidirect |
| 19. #14583170 | C22 | semidirect |
| 23. #14582720 | C22 | semidirect |
| 24. #14582711 | C22 | semidirect |
| 25. #14582682 | C22 | semidirect |
| 27. C43×#443 | C22 | semidirect |
| 28. C43×#368 | C22 | semidirect |
| 29. C43×#359 | C22 | semidirect |
| 30. C4×C16×C43 | C22 | semidirect |
| 58. Q32×C43 | D4 | semidirect |
| 59. SD32×C43 | D4 | semidirect |
| 60. D16×C43 | D4 | semidirect |
| 144. #2178 | D43 | semidirect |
| 166. #443 | C2×D43 | semidirect |
| 167. #368 | C2×D43 | semidirect |
| 170. #359 | C2×D43 | semidirect |
| 172. C4×C16 | C2×D43 | semidirect |
| 173. C43 | #33858 | semidirect |
| 190. Q32 | D172 | semidirect |
| 192. SD32 | D172 | semidirect |
| 197. D16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147733 | 2 |
| #19146395 | 2 |
| #19136845 | 2 |
| #19136716 | 2 |
| #19136671 | 2 |
| #19136553 | 2 |
| #19136433 | 2 |
| C43×#2178 | 2 |
| #33858 | 43 |