Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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×Q16×D89 | C2 | semidirect |
| 3. C4⋊Q8×D89 | C2 | semidirect |
| 5. #19151993 | C2 | semidirect |
| 6. #19151992 | C2 | semidirect |
| 7. #19151991 | C2 | semidirect |
| 8. #19151990 | C2 | semidirect |
| 9. #19151989 | C2 | semidirect |
| 10. #97×D89 | C2 | semidirect |
| 11. #497×C89 | C2 | semidirect |
| 15. C2×Dic356 | C22 | semidirect |
| 16. C2×#13083564 | C22 | semidirect |
| 17. C2×#13083564 | C22 | semidirect |
| 24. #15668012 | C22 | semidirect |
| 26. #15668010 | C22 | semidirect |
| 34. #15667923 | C22 | semidirect |
| 35. #15667922 | C22 | semidirect |
| 36. C2×Q16×C89 | C22 | semidirect |
| 38. C4⋊Q8×C89 | C22 | semidirect |
| 40. #97×C89 | C22 | semidirect |
| 130. D89 | #497 | direct (N × H) |
| 132. C89 | C2×#497 | semidirect |
| 142. #497 | D89 | direct (N × H) |
| 151. C2×Q16 | C2×D89 | semidirect |
| 161. C4⋊Q8 | C2×D89 | semidirect |
| 172. #97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D89 | 2 |
| C2×SD16×D89 | 2 |
| C4⋊Q8×D89 | 2 |
| #124×D89 | 2 |
| #19151993 | 2 |
| #19151992 | 2 |
| #19151991 | 2 |
| #19151990 | 2 |
| #19151989 | 2 |
| #97×D89 | 2 |
| #497×C89 | 2 |
| C2×#497 | 89 |