Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. #19151936 | C2 | semidirect |
| 3. #19151895 | C2 | semidirect |
| 4. #19151800 | C2 | semidirect |
| 6. #19151696 | C2 | semidirect |
| 7. C4×#13083561 | C2 | semidirect |
| 8. #19151659 | C2 | semidirect |
| 9. #541×C89 | C2 | semidirect |
| 18. #15667945 | C22 | semidirect |
| 19. #15667943 | C22 | semidirect |
| 20. C4⋊#10623494 | C22 | semidirect |
| 21. #15667936 | C22 | semidirect |
| 22. #15667936 | C22 | semidirect |
| 26. #15667923 | C22 | semidirect |
| 27. C4×#10623494 | C22 | semidirect |
| 28. C4⋊Q8×C89 | C22 | semidirect |
| 31. #125×C89 | C22 | semidirect |
| 33. C4×Q8×C89 | C22 | semidirect |
| 103. C89 | #3123 | semidirect |
| 104. #541 | D89 | semidirect |
| 116. C4⋊Q8 | C2×D89 | semidirect |
| 119. #125 | C2×D89 | semidirect |
| 121. C4×Q8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152072 | 2 |
| #19151936 | 2 |
| #19151895 | 2 |
| #19151800 | 2 |
| #19151748 | 2 |
| #19151696 | 2 |
| C4×#13083561 | 2 |
| #19151659 | 2 |
| #541×C89 | 2 |
| #3123 | 89 |