Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19152143 | C2 | semidirect |
| 2. C2×#15668008 | C2 | semidirect |
| 3. #19151973 | C2 | semidirect |
| 4. #19151943 | C2 | semidirect |
| 5. #19151792 | C2 | semidirect |
| 6. #19151791 | C2 | semidirect |
| 7. #19151734 | C2 | semidirect |
| 8. #19151732 | C2 | semidirect |
| 9. #19151731 | C2 | semidirect |
| 10. #19151648 | C2 | semidirect |
| 11. #447×C89 | C2 | semidirect |
| 16. C2×D712 | C22 | semidirect |
| 17. C2×#13083559 | C22 | semidirect |
| 18. C2×#13083559 | C22 | semidirect |
| 19. #15668011 | C22 | semidirect |
| 24. #15668008 | C22 | semidirect |
| 28. D4×Dic89 | C22 | semidirect |
| 29. #15667974 | C22 | semidirect |
| 32. #15667941 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667932 | C22 | semidirect |
| 37. C8×Dic89 | C22 | semidirect |
| 39. C2×D8×C89 | C22 | semidirect |
| 41. #102×C89 | C22 | semidirect |
| 117. C2×Dic89 | D8 | semidirect |
| 165. C89 | #3205 | semidirect |
| 175. #447 | D89 | semidirect |
| 185. C2×D8 | C2×D89 | semidirect |
| 204. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152143 | 2 |
| C2×#15668008 | 2 |
| #19151973 | 2 |
| #19151943 | 2 |
| #19151792 | 2 |
| #19151791 | 2 |
| #19151734 | 2 |
| #19151732 | 2 |
| #19151731 | 2 |
| #19151648 | 2 |
| #447×C89 | 2 |
| #3205 | 89 |