Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19152081 | C2 | semidirect |
| 3. #19151923 | C2 | semidirect |
| 4. #19151923 | C2 | semidirect |
| 5. #19151917 | C2 | semidirect |
| 6. #19151912 | C2 | semidirect |
| 7. #19151640 | C2 | semidirect |
| 8. #19151636 | C2 | semidirect |
| 9. #19151604 | C2 | semidirect |
| 10. C2×#15667934 | C2 | semidirect |
| 11. #408×C89 | C2 | semidirect |
| 23. #15667971 | C22 | semidirect |
| 25. C2×C4⋊Dic89 | C22 | semidirect |
| 26. #15667946 | C22 | semidirect |
| 27. #15667946 | C22 | semidirect |
| 28. #15667946 | C22 | semidirect |
| 29. #15667944 | C22 | semidirect |
| 30. #15667944 | C22 | semidirect |
| 31. #15667944 | C22 | semidirect |
| 39. C22⋊C8×C89 | C22 | semidirect |
| 40. C22⋊C8×C89 | C22 | semidirect |
| 135. C89 | #3096 | semidirect |
| 146. #408 | D89 | semidirect |
| 174. C22⋊C8 | C2×D89 | semidirect |
| 175. C22⋊C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152162 | 2 |
| #19152081 | 2 |
| #19151923 | 2 |
| #19151917 | 2 |
| #19151912 | 2 |
| #19151640 | 2 |
| #19151636 | 2 |
| #19151604 | 2 |
| C2×#15667934 | 2 |
| #408×C89 | 2 |
| #3096 | 89 |