Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #19152078 | C2 | semidirect |
| 3. #19151925 | C2 | semidirect |
| 4. #19151924 | C2 | semidirect |
| 5. #19151918 | C2 | semidirect |
| 6. #19151913 | C2 | semidirect |
| 7. #19151641 | C2 | semidirect |
| 8. #19151602 | C2 | semidirect |
| 9. C2×#15667934 | C2 | semidirect |
| 10. #19151564 | C2 | semidirect |
| 11. #427×C89 | C2 | semidirect |
| 23. #15667970 | C22 | semidirect |
| 25. C4⋊C4×D89 | C22 | semidirect |
| 26. #15667945 | C22 | semidirect |
| 27. #15667943 | C22 | semidirect |
| 32. #15667924 | C22 | semidirect |
| 33. #15667924 | C22 | semidirect |
| 37. #107×C89 | C22 | semidirect |
| 38. #107×C89 | C22 | semidirect |
| 39. #106×C89 | C22 | semidirect |
| 40. #106×C89 | C22 | semidirect |
| 135. C89 | #3096 | semidirect |
| 143. #427 | D89 | semidirect |
| 165. #107 | C2×D89 | semidirect |
| 166. #107 | C2×D89 | semidirect |
| 168. #106 | C2×D89 | semidirect |
| 169. #106 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152167 | 2 |
| #19152078 | 2 |
| #19151925 | 2 |
| #19151924 | 2 |
| #19151918 | 2 |
| #19151913 | 2 |
| #19151641 | 2 |
| #19151602 | 2 |
| C2×#15667934 | 2 |
| #19151564 | 2 |
| #427×C89 | 2 |
| #3096 | 89 |