Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19152308 | C2 | semidirect |
| 3. #19151944 | C2 | semidirect |
| 4. #19151915 | C2 | semidirect |
| 5. #19151889 | C2 | semidirect |
| 6. #19151824 | C2 | semidirect |
| 7. #19151747 | C2 | semidirect |
| 8. C4×#13083561 | C2 | semidirect |
| 9. #19151663 | C2 | semidirect |
| 10. #102×D89 | C2 | semidirect |
| 11. #460×C89 | C2 | semidirect |
| 15. C2×C8×D89 | C22 | semidirect |
| 16. #15668012 | C22 | semidirect |
| 19. #15667988 | C22 | semidirect |
| 26. C4⋊C4×D89 | C22 | semidirect |
| 27. #15667944 | C22 | semidirect |
| 28. #15667943 | C22 | semidirect |
| 29. #15667936 | C22 | semidirect |
| 31. #15667933 | C22 | semidirect |
| 32. #15667933 | C22 | semidirect |
| 34. #15667924 | C22 | semidirect |
| 35. C4×#10623494 | C22 | semidirect |
| 36. C2×SD16×C89 | C22 | semidirect |
| 38. C4×Q8×C89 | C22 | semidirect |
| 39. C4⋊C8×C89 | C22 | semidirect |
| 40. #102×C89 | C22 | semidirect |
| 100. D356 | SD16 | semidirect |
| 137. C89 | #3295 | semidirect |
| 144. #460 | D89 | semidirect |
| 152. C2×SD16 | C2×D89 | semidirect |
| 162. C4×Q8 | C2×D89 | semidirect |
| 169. C4⋊C8 | C2×D89 | semidirect |
| 175. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152308 | 2 |
| #19152233 | 2 |
| #19151944 | 2 |
| #19151915 | 2 |
| #19151889 | 2 |
| #19151824 | 2 |
| #19151747 | 2 |
| C4×#13083561 | 2 |
| #19151663 | 2 |
| #102×D89 | 2 |
| #460×C89 | 2 |
| #3295 | 89 |