Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19152108 | C2 | semidirect |
| 2. C2×#15667983 | C2 | semidirect |
| 3. #19151934 | C2 | semidirect |
| 4. #19151920 | C2 | semidirect |
| 5. #19151914 | C2 | semidirect |
| 6. #19151831 | C2 | semidirect |
| 7. #19151826 | C2 | semidirect |
| 8. #19151749 | C2 | semidirect |
| 9. #19151740 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #447×C89 | C2 | semidirect |
| 12. C2×#13083573 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 16. C2×C8×D89 | C22 | semidirect |
| 18. #15667992 | C22 | semidirect |
| 24. #15667983 | C22 | semidirect |
| 28. #15667970 | C22 | semidirect |
| 31. #15667946 | C22 | semidirect |
| 32. #15667943 | C22 | semidirect |
| 33. #15667937 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667933 | C22 | semidirect |
| 37. #15667924 | C22 | semidirect |
| 39. C2×D8×C89 | C22 | semidirect |
| 41. #102×C89 | C22 | semidirect |
| 159. C89 | #3188 | semidirect |
| 169. #447 | D89 | semidirect |
| 176. C2×D8 | C2×D89 | semidirect |
| 198. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152108 | 2 |
| C2×#15667983 | 2 |
| #19151934 | 2 |
| #19151920 | 2 |
| #19151914 | 2 |
| #19151831 | 2 |
| #19151826 | 2 |
| #19151749 | 2 |
| #19151740 | 2 |
| C22⋊C8×D89 | 2 |
| #447×C89 | 2 |
| #3188 | 89 |