Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 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. #19152401 | C2 | semidirect |
| 2. #19152400 | C2 | semidirect |
| 3. #19151973 | C2 | semidirect |
| 4. #19151868 | C2 | semidirect |
| 5. #19151866 | C2 | semidirect |
| 6. #19151865 | C2 | semidirect |
| 7. #19151766 | C2 | semidirect |
| 8. #19151764 | C2 | semidirect |
| 9. #19151715 | C2 | semidirect |
| 10. #19151713 | C2 | semidirect |
| 11. #576×C89 | C2 | semidirect |
| 12. #15668058 | C22 | semidirect |
| 15. #15668038 | C22 | semidirect |
| 17. #15668037 | C22 | semidirect |
| 18. #15668037 | C22 | semidirect |
| 22. C2×D712 | C22 | semidirect |
| 24. C2×#13083559 | C22 | semidirect |
| 26. #15668019 | C22 | semidirect |
| 27. #15668018 | C22 | semidirect |
| 28. #15668008 | C22 | semidirect |
| 29. #15667948 | C22 | semidirect |
| 30. #15667947 | C22 | semidirect |
| 31. #15667939 | C22 | semidirect |
| 32. #15667939 | C22 | semidirect |
| 33. #15667938 | C22 | semidirect |
| 34. #15667929 | C22 | semidirect |
| 35. #15667928 | C22 | semidirect |
| 36. C8×Dic89 | C22 | semidirect |
| 37. H(5,𝔽2)×C89 | C22 | semidirect |
| 39. AGL(1,ℤ/8)×C89 | C22 | semidirect |
| 43. C2×D8×C89 | C22 | semidirect |
| 44. #131×C89 | C22 | semidirect |
| 53. #13083564 | D4 | semidirect |
| 55. #13083562 | D4 | semidirect |
| 58. #13083561 | D4 | semidirect |
| 66. #13083559 | D4 | semidirect |
| 83. Q16×C89 | D4 | semidirect |
| 85. SD16×C89 | D4 | semidirect |
| 89. D8×C89 | D4 | semidirect |
| 154. C89 | #3292 | semidirect |
| 157. #576 | D89 | semidirect |
| 167. H(5,𝔽2) | C2×D89 | semidirect |
| 175. AGL(1,ℤ/8) | C2×D89 | semidirect |
| 186. C2×D8 | C2×D89 | semidirect |
| 189. #131 | C2×D89 | semidirect |
| 216. Q16 | C22⋊D89 | semidirect |
| 223. SD16 | C22⋊D89 | semidirect |
| 235. D8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152401 | 2 |
| #19152400 | 2 |
| #19151973 | 2 |
| #19151868 | 2 |
| #19151866 | 2 |
| #19151865 | 2 |
| #19151766 | 2 |
| #19151764 | 2 |
| #19151715 | 2 |
| #19151713 | 2 |
| #576×C89 | 2 |
| #3292 | 89 |