Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668032 | C2 | semidirect |
| 2. #19152165 | C2 | semidirect |
| 3. #19152081 | C2 | semidirect |
| 4. #19151818 | C2 | semidirect |
| 5. #19151811 | C2 | semidirect |
| 6. #19151796 | C2 | semidirect |
| 7. #19151791 | C2 | semidirect |
| 8. #19151626 | C2 | semidirect |
| 9. #19151600 | C2 | semidirect |
| 10. C2×#15667933 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C89 | C2 | semidirect |
| 14. C2×#13083564 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 16. C2×#13083561 | C22 | semidirect |
| 17. C2×#13083559 | C22 | semidirect |
| 24. Q8×Dic89 | C22 | semidirect |
| 26. D4×Dic89 | C22 | semidirect |
| 31. #15667941 | C22 | semidirect |
| 32. #15667941 | C22 | semidirect |
| 33. #15667937 | C22 | semidirect |
| 34. #15667934 | C22 | semidirect |
| 73. #41×C89 | D4 | semidirect |
| 155. C89 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D89 | semidirect |
| 202. #41 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668032 | 2 |
| #19152165 | 2 |
| #19152081 | 2 |
| #19151818 | 2 |
| #19151811 | 2 |
| #19151796 | 2 |
| #19151791 | 2 |
| #19151626 | 2 |
| #19151600 | 2 |
| C2×#15667933 | 2 |
| C2×AGL(1,ℤ/8)×C89 | 2 |
| #3045 | 89 |