Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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×#15668034 | C2 | semidirect |
| 2. C2×D8×D89 | C2 | semidirect |
| 3. #19152245 | C2 | semidirect |
| 4. #19151981 | C2 | semidirect |
| 5. #19151840 | C2 | semidirect |
| 6. #19151812 | C2 | semidirect |
| 7. #19151750 | C2 | semidirect |
| 8. #19151741 | C2 | semidirect |
| 9. #19151680 | C2 | semidirect |
| 10. C8×C22⋊D89 | C2 | semidirect |
| 11. #466×C89 | C2 | semidirect |
| 12. C2×#13083574 | C22 | semidirect |
| 15. C2×Dic356 | C22 | semidirect |
| 16. C2×#13083563 | C22 | semidirect |
| 17. C2×#13083562 | C22 | semidirect |
| 22. #15667999 | C22 | semidirect |
| 27. #15667974 | C22 | semidirect |
| 30. #15667941 | C22 | semidirect |
| 31. #15667935 | C22 | semidirect |
| 32. #15667932 | C22 | semidirect |
| 33. C22⋊#10623494 | C22 | semidirect |
| 35. C8×Dic89 | C22 | semidirect |
| 37. C22×C8×C89 | C22 | semidirect |
| 38. #121×C89 | C22 | semidirect |
| 39. #107×C89 | C22 | semidirect |
| 40. #102×C89 | C22 | semidirect |
| 57. D712 | D4 | semidirect |
| 127. C2×D89 | #135 | semidirect |
| 144. C89 | #3280 | semidirect |
| 150. #466 | D89 | semidirect |
| 167. C22×C8 | C2×D89 | semidirect |
| 172. #121 | C2×D89 | semidirect |
| 177. #107 | C2×D89 | semidirect |
| 181. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668034 | 2 |
| C2×D8×D89 | 2 |
| #19152245 | 2 |
| #19151981 | 2 |
| #19151840 | 2 |
| #19151812 | 2 |
| #19151750 | 2 |
| #19151741 | 2 |
| #19151680 | 2 |
| C8×C22⋊D89 | 2 |
| #466×C89 | 2 |
| #3280 | 89 |