Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15668037 | C2 | semidirect |
| 2. C22×#13083559 | C2 | semidirect |
| 3. #19152162 | C2 | semidirect |
| 4. #19151743 | C2 | semidirect |
| 5. #19151732 | C2 | semidirect |
| 6. #19151603 | C2 | semidirect |
| 7. #19151594 | C2 | semidirect |
| 8. #19151565 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C89 | C2 | semidirect |
| 10. C22×D356 | C22 | semidirect |
| 12. C2×#13083561 | C22 | semidirect |
| 14. C2×#13083559 | C22 | semidirect |
| 15. C2×#13083559 | C22 | semidirect |
| 16. C2×#13083558 | C22 | semidirect |
| 17. C22×#10623494 | C22 | semidirect |
| 20. #15667986 | C22 | semidirect |
| 22. #15667971 | C22 | semidirect |
| 23. #15667936 | C22 | semidirect |
| 24. #15667933 | C22 | semidirect |
| 25. #15667933 | C22 | semidirect |
| 26. C22⋊#10623494 | C22 | semidirect |
| 32. C2×#41×C89 | C22 | semidirect |
| 36. C22×D4×C89 | C22 | semidirect |
| 62. #41×C89 | D4 | semidirect |
| 76. C2×D4×C89 | D4 | semidirect |
| 152. C89 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D89 | semidirect |
| 167. C2×#41 | C2×D89 | semidirect |
| 172. C22×D4 | C2×D89 | semidirect |
| 198. #41 | C22⋊D89 | semidirect |
| 217. C2×D4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668037 | 2 |
| C22×#13083559 | 2 |
| #19152162 | 2 |
| #19151743 | 2 |
| #19151732 | 2 |
| #19151603 | 2 |
| #19151594 | 2 |
| #19151565 | 2 |
| C2×H(5,𝔽2)×C89 | 2 |
| #3008 | 89 |