Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668040 | C2 | semidirect |
| 2. #19152176 | C2 | semidirect |
| 3. #19152162 | C2 | semidirect |
| 4. #19151851 | C2 | semidirect |
| 5. #19151844 | C2 | semidirect |
| 6. #19151834 | C2 | semidirect |
| 7. #19151827 | C2 | semidirect |
| 8. #19151640 | C2 | semidirect |
| 9. #19151595 | C2 | semidirect |
| 10. C2×#15667934 | C2 | semidirect |
| 11. C2×#131×C89 | C2 | semidirect |
| 19. #15667991 | C22 | semidirect |
| 23. #15667986 | C22 | semidirect |
| 29. #15667946 | C22 | semidirect |
| 30. #15667944 | C22 | semidirect |
| 31. #15667937 | C22 | semidirect |
| 32. #15667937 | C22 | semidirect |
| 35. #15667934 | C22 | semidirect |
| 36. #15667934 | C22 | semidirect |
| 40. C2×M16×C89 | C22 | semidirect |
| 42. C22×C8×C89 | C22 | semidirect |
| 79. M16×C89 | D4 | semidirect |
| 152. C89 | #3062 | semidirect |
| 154. C2×#131 | D89 | semidirect |
| 172. C2×M16 | C2×D89 | semidirect |
| 174. C22×C8 | C2×D89 | semidirect |
| 220. M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668040 | 2 |
| #19152176 | 2 |
| #19152162 | 2 |
| #19151851 | 2 |
| #19151844 | 2 |
| #19151834 | 2 |
| #19151827 | 2 |
| #19151640 | 2 |
| #19151595 | 2 |
| C2×#15667934 | 2 |
| C2×#131×C89 | 2 |
| #3062 | 89 |