Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. C2×#15667988 | C2 | semidirect |
| 3. #19151937 | C2 | semidirect |
| 4. #19151929 | C2 | semidirect |
| 5. #19151909 | C2 | semidirect |
| 6. #19151838 | C2 | semidirect |
| 7. #19151824 | C2 | semidirect |
| 8. #19151757 | C2 | semidirect |
| 9. #19151754 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #448×C89 | C2 | semidirect |
| 14. C2×#13083564 | C22 | semidirect |
| 31. #15667945 | C22 | semidirect |
| 32. #15667944 | C22 | semidirect |
| 33. #15667937 | C22 | semidirect |
| 34. #15667936 | C22 | semidirect |
| 35. #15667933 | C22 | semidirect |
| 39. C2×SD16×C89 | C22 | semidirect |
| 41. #103×C89 | C22 | semidirect |
| 150. C89 | #3190 | semidirect |
| 160. #448 | D89 | semidirect |
| 166. C2×SD16 | C2×D89 | semidirect |
| 188. #103 | 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×#15667988 | 2 |
| #19151937 | 2 |
| #19151929 | 2 |
| #19151909 | 2 |
| #19151838 | 2 |
| #19151824 | 2 |
| #19151757 | 2 |
| #19151754 | 2 |
| C22⋊C8×D89 | 2 |
| #448×C89 | 2 |
| #3190 | 89 |