Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
786 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15667995 | C2 | semidirect |
| 3. C2×#15667971 | C2 | semidirect |
| 4. #19151521 | C2 | semidirect |
| 5. #19151514 | C2 | semidirect |
| 6. #19151498 | C2 | semidirect |
| 7. #19151492 | C2 | semidirect |
| 8. #19151477 | C2 | semidirect |
| 9. #19151471 | C2 | semidirect |
| 10. #19151454 | C2 | semidirect |
| 11. C22×C22⋊C4×C89 | C2 | semidirect |
| 17. C2×C4⋊Dic89 | C22 | semidirect |
| 18. C2×#13083553 | C22 | semidirect |
| 19. C2×#13083553 | C22 | semidirect |
| 20. C2×#13083553 | C22 | semidirect |
| 27. C2×#13083551 | C22 | semidirect |
| 28. C2×#13083551 | C22 | semidirect |
| 29. C2×#13083551 | C22 | semidirect |
| 30. C2×C4×Dic89 | C22 | semidirect |
| 31. #15667919 | C22 | semidirect |
| 32. #15667919 | C22 | semidirect |
| 76. C22×C4×C89 | D4 | semidirect |
| 171. C89 | #2411 | semidirect |
| 175. C22×C22⋊C4 | D89 | semidirect |
| 233. C22×C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667995 | 2 |
| C2×#15667981 | 2 |
| C2×#15667971 | 2 |
| #19151521 | 2 |
| #19151514 | 2 |
| #19151498 | 2 |
| #19151492 | 2 |
| #19151477 | 2 |
| #19151471 | 2 |
| #19151454 | 2 |
| C22×C22⋊C4×C89 | 2 |
| #2411 | 89 |