Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15667999 | C2 | semidirect |
| 3. #19151979 | C2 | semidirect |
| 4. #19151951 | C2 | semidirect |
| 5. #19151818 | C2 | semidirect |
| 6. #19151812 | C2 | semidirect |
| 7. #19151753 | C2 | semidirect |
| 8. #19151739 | C2 | semidirect |
| 10. #19151648 | C2 | semidirect |
| 11. #450×C89 | C2 | semidirect |
| 13. C2×#13083564 | C22 | semidirect |
| 14. C2×#13083563 | C22 | semidirect |
| 17. #15668003 | C22 | semidirect |
| 18. #15668001 | C22 | semidirect |
| 25. Q8×Dic89 | C22 | semidirect |
| 26. #15667974 | C22 | semidirect |
| 32. #15667941 | C22 | semidirect |
| 33. #15667937 | C22 | semidirect |
| 34. #15667935 | C22 | semidirect |
| 37. C8×Dic89 | C22 | semidirect |
| 144. C89 | #3211 | semidirect |
| 152. #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×#15667999 | 2 |
| #19151979 | 2 |
| #19151951 | 2 |
| #19151818 | 2 |
| #19151812 | 2 |
| #19151753 | 2 |
| #19151739 | 2 |
| #19151732 | 2 |
| #19151648 | 2 |
| #450×C89 | 2 |
| #3211 | 89 |