Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #19152434 | C2 | semidirect |
| 2. #19152413 | C2 | semidirect |
| 3. #19152406 | C2 | semidirect |
| 4. #19152396 | C2 | semidirect |
| 5. C2×#15668043 | C2 | semidirect |
| 6. #19152365 | C2 | semidirect |
| 7. C2×2−1+4×C89 | C2 | semidirect |
| 9. #15668059 | C22 | semidirect |
| 10. #15668058 | C22 | semidirect |
| 14. #15668043 | C22 | semidirect |
| 15. #15668043 | C22 | semidirect |
| 16. #15668042 | C22 | semidirect |
| 17. #15668038 | C22 | semidirect |
| 18. #15668037 | C22 | semidirect |
| 19. #15668032 | C22 | semidirect |
| 20. C2×#13083564 | C22 | semidirect |
| 21. C2×#13083561 | C22 | semidirect |
| 22. #15668019 | C22 | semidirect |
| 23. C2×#13083558 | C22 | semidirect |
| 25. 2−1+4×C89 | C22 | semidirect |
| 28. C2×#41×C89 | C22 | semidirect |
| 30. C22×Q8×C89 | C22 | semidirect |
| 113. C89 | #3586 | semidirect |
| 115. C2×2−1+4 | D89 | semidirect |
| 124. 2−1+4 | C2×D89 | semidirect |
| 131. C2×#41 | C2×D89 | semidirect |
| 133. C22×Q8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152434 | 2 |
| #19152413 | 2 |
| #19152406 | 2 |
| #19152396 | 2 |
| C2×#15668043 | 2 |
| #19152365 | 2 |
| C2×2−1+4×C89 | 2 |
| #3586 | 89 |