Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#15668039 | C2 | semidirect |
| 2. #19152270 | C2 | semidirect |
| 3. #19152233 | C2 | semidirect |
| 4. #19151974 | C2 | semidirect |
| 5. #19151850 | C2 | semidirect |
| 6. #19151794 | C2 | semidirect |
| 7. #19151742 | C2 | semidirect |
| 8. #19151733 | C2 | semidirect |
| 9. C4×#13083561 | C2 | semidirect |
| 10. #19151675 | C2 | semidirect |
| 11. #460×C89 | C2 | semidirect |
| 12. C2×#13083575 | C22 | semidirect |
| 18. C2×#13083559 | C22 | semidirect |
| 19. C2×#13083559 | C22 | semidirect |
| 20. C2×#13083557 | C22 | semidirect |
| 22. #15668009 | C22 | semidirect |
| 24. #15667987 | C22 | semidirect |
| 31. #15667943 | C22 | semidirect |
| 32. #15667936 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 35. #15667924 | C22 | semidirect |
| 36. C4×#10623494 | C22 | semidirect |
| 37. C2×SD16×C89 | C22 | semidirect |
| 39. C4×Q8×C89 | C22 | semidirect |
| 40. C4⋊C8×C89 | C22 | semidirect |
| 41. #102×C89 | C22 | semidirect |
| 60. #13083561 | D4 | semidirect |
| 91. Q8×C89 | C2×D4 | semidirect |
| 120. #10623494 | C2×D4 | semidirect |
| 138. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 151. C89 | #3274 | semidirect |
| 157. #460 | D89 | semidirect |
| 168. C2×SD16 | C2×D89 | semidirect |
| 181. C4×Q8 | C2×D89 | semidirect |
| 186. C4⋊C8 | C2×D89 | semidirect |
| 190. #102 | C2×D89 | semidirect |
| 242. Q8 | D4×D89 | semidirect |
| 291. C4 | #15668039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668039 | 2 |
| #19152270 | 2 |
| #19152233 | 2 |
| #19151974 | 2 |
| #19151850 | 2 |
| #19151794 | 2 |
| #19151742 | 2 |
| #19151733 | 2 |
| C4×#13083561 | 2 |
| #19151675 | 2 |
| #460×C89 | 2 |
| #3274 | 89 |