Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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. #19152396 | C2 | semidirect |
| 2. #19152165 | C2 | semidirect |
| 3. #19151776 | C2 | semidirect |
| 4. #19151766 | C2 | semidirect |
| 5. #19151615 | C2 | semidirect |
| 6. C2×#15667929 | C2 | semidirect |
| 7. C2×H(5,𝔽2)×C89 | C2 | semidirect |
| 8. C2×#13083574 | C22 | semidirect |
| 10. #15668042 | C22 | semidirect |
| 12. #15668037 | C22 | semidirect |
| 14. C2×#13083558 | C22 | semidirect |
| 15. #15668008 | C22 | semidirect |
| 16. #15667999 | C22 | semidirect |
| 19. #15667971 | C22 | semidirect |
| 20. #15667939 | C22 | semidirect |
| 21. #15667929 | C22 | semidirect |
| 32. C2×Dic178 | C23 | semidirect |
| 33. C2×D356 | C23 | semidirect |
| 42. #13083558 | C23 | semidirect |
| 47. C4×Dic89 | C23 | semidirect |
| 54. #41×C89 | D4 | semidirect |
| 56. C2×Q8×C89 | D4 | semidirect |
| 66. C2×D4×C89 | D4 | semidirect |
| 132. C89 | #3019 | semidirect |
| 133. C2×H(5,𝔽2) | D89 | semidirect |
| 170. #41 | C22⋊D89 | semidirect |
| 173. C2×Q8 | C22⋊D89 | semidirect |
| 186. C2×D4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152396 | 2 |
| #19152165 | 2 |
| #19151776 | 2 |
| #19151766 | 2 |
| #19151615 | 2 |
| C2×#15667929 | 2 |
| C2×H(5,𝔽2)×C89 | 2 |
| #3019 | 89 |