Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668038 | C2 | semidirect |
| 2. #19152165 | C2 | semidirect |
| 3. #19152073 | C2 | semidirect |
| 4. #19151811 | C2 | semidirect |
| 5. #19151791 | C2 | semidirect |
| 6. #19151624 | C2 | semidirect |
| 7. #19151603 | C2 | semidirect |
| 8. #19151595 | C2 | semidirect |
| 9. C22×D8×C89 | C2 | semidirect |
| 12. C2×#13083562 | C22 | semidirect |
| 13. C2×#13083559 | C22 | semidirect |
| 15. #15668008 | C22 | semidirect |
| 16. #15667999 | C22 | semidirect |
| 20. D4×Dic89 | C22 | semidirect |
| 24. #15667941 | C22 | semidirect |
| 25. #15667937 | C22 | semidirect |
| 26. #15667934 | C22 | semidirect |
| 27. #15667933 | C22 | semidirect |
| 60. C2×D4×C89 | D4 | semidirect |
| 122. C89 | #3041 | semidirect |
| 124. C22×D8 | D89 | semidirect |
| 168. 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×#15668038 | 2 |
| #19152165 | 2 |
| #19152073 | 2 |
| #19151811 | 2 |
| #19151791 | 2 |
| #19151624 | 2 |
| #19151603 | 2 |
| #19151595 | 2 |
| C22×D8×C89 | 2 |
| #3041 | 89 |