Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19152406 | C2 | semidirect |
| 2. #19152400 | C2 | semidirect |
| 3. #19151983 | C2 | semidirect |
| 4. #19151870 | C2 | semidirect |
| 5. #19151868 | C2 | semidirect |
| 6. #19151863 | C2 | semidirect |
| 7. #19151774 | C2 | semidirect |
| 8. #19151771 | C2 | semidirect |
| 9. #19151715 | C2 | semidirect |
| 10. #19151713 | C2 | semidirect |
| 11. #578×C89 | C2 | semidirect |
| 18. #15668037 | C22 | semidirect |
| 23. C2×#13083561 | C22 | semidirect |
| 26. #15668019 | C22 | semidirect |
| 28. #15668001 | C22 | semidirect |
| 29. #15667948 | C22 | semidirect |
| 30. #15667947 | C22 | semidirect |
| 31. #15667939 | C22 | semidirect |
| 32. #15667939 | C22 | semidirect |
| 34. #15667931 | C22 | semidirect |
| 35. #15667928 | C22 | semidirect |
| 36. C8×Dic89 | C22 | semidirect |
| 37. 2−1+4×C89 | C22 | semidirect |
| 39. #137×C89 | C22 | semidirect |
| 43. C2×Q16×C89 | C22 | semidirect |
| 44. #131×C89 | C22 | semidirect |
| 150. C89 | #3290 | semidirect |
| 151. #578 | D89 | semidirect |
| 162. 2−1+4 | C2×D89 | semidirect |
| 167. #137 | C2×D89 | semidirect |
| 178. C2×Q16 | C2×D89 | semidirect |
| 185. #131 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152406 | 2 |
| #19152400 | 2 |
| #19151983 | 2 |
| #19151870 | 2 |
| #19151868 | 2 |
| #19151863 | 2 |
| #19151774 | 2 |
| #19151771 | 2 |
| #19151715 | 2 |
| #19151713 | 2 |
| #578×C89 | 2 |
| #3290 | 89 |