Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D89 | C2 | semidirect |
| 2. C2×#15668018 | C2 | semidirect |
| 3. #19152164 | C2 | semidirect |
| 4. #19151850 | C2 | semidirect |
| 5. #19151849 | C2 | semidirect |
| 6. #19151835 | C2 | semidirect |
| 7. #19151834 | C2 | semidirect |
| 8. #19151831 | C2 | semidirect |
| 9. #19151635 | C2 | semidirect |
| 10. #19151601 | C2 | semidirect |
| 11. #466×C89 | C2 | semidirect |
| 18. C2×#13083558 | C22 | semidirect |
| 20. C2×#13083557 | C22 | semidirect |
| 22. C2×C8×D89 | C22 | semidirect |
| 25. #15667987 | C22 | semidirect |
| 26. #15667986 | C22 | semidirect |
| 27. #15667983 | C22 | semidirect |
| 31. #15667946 | C22 | semidirect |
| 32. #15667943 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667932 | C22 | semidirect |
| 37. C22×C8×C89 | C22 | semidirect |
| 38. #121×C89 | C22 | semidirect |
| 39. #107×C89 | C22 | semidirect |
| 40. #102×C89 | C22 | semidirect |
| 65. C8×D89 | D4 | semidirect |
| 151. C89 | #3058 | semidirect |
| 160. #466 | D89 | semidirect |
| 175. C22×C8 | C2×D89 | semidirect |
| 181. #121 | C2×D89 | semidirect |
| 186. #107 | C2×D89 | semidirect |
| 191. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D89 | 2 |
| C2×#15668018 | 2 |
| #19152164 | 2 |
| #19151850 | 2 |
| #19151849 | 2 |
| #19151835 | 2 |
| #19151834 | 2 |
| #19151831 | 2 |
| #19151635 | 2 |
| #19151601 | 2 |
| #466×C89 | 2 |
| #3058 | 89 |