Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19152134 | C2 | semidirect |
| 2. C2×D4×Dic89 | C2 | semidirect |
| 3. #19151926 | C2 | semidirect |
| 4. #19151912 | C2 | semidirect |
| 5. #19151896 | C2 | semidirect |
| 6. #19151815 | C2 | semidirect |
| 8. #19151707 | C2 | semidirect |
| 9. #19151699 | C2 | semidirect |
| 10. #19151652 | C2 | semidirect |
| 11. #450×C89 | C2 | semidirect |
| 15. #15668003 | C22 | semidirect |
| 16. #15668001 | C22 | semidirect |
| 19. Q8×Dic89 | C22 | semidirect |
| 24. #15667974 | C22 | semidirect |
| 30. #15667946 | C22 | semidirect |
| 31. #15667943 | C22 | semidirect |
| 32. #15667941 | C22 | semidirect |
| 33. #15667936 | C22 | semidirect |
| 34. #15667934 | C22 | semidirect |
| 37. #15667922 | C22 | semidirect |
| 141. C89 | #3114 | semidirect |
| 148. #450 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152134 | 2 |
| C2×D4×Dic89 | 2 |
| #19151926 | 2 |
| #19151912 | 2 |
| #19151896 | 2 |
| #19151815 | 2 |
| #19151732 | 2 |
| #19151707 | 2 |
| #19151699 | 2 |
| #19151652 | 2 |
| #450×C89 | 2 |
| #3114 | 89 |