Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15668031 | C2 | semidirect |
| 2. #19152242 | C2 | semidirect |
| 3. #19151981 | C2 | semidirect |
| 4. #19151839 | C2 | semidirect |
| 5. #19151831 | C2 | semidirect |
| 6. #19151811 | C2 | semidirect |
| 7. #19151749 | C2 | semidirect |
| 8. #19151740 | C2 | semidirect |
| 9. D8×Dic89 | C2 | semidirect |
| 10. C8×C22⋊D89 | C2 | semidirect |
| 11. C22×D8×C89 | C2 | semidirect |
| 12. C2×#13083573 | C22 | semidirect |
| 14. C2×Dic356 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 16. C2×#13083562 | C22 | semidirect |
| 17. C2×C8×D89 | C22 | semidirect |
| 18. #15667999 | C22 | semidirect |
| 22. #15667983 | C22 | semidirect |
| 24. D4×Dic89 | C22 | semidirect |
| 27. #15667946 | C22 | semidirect |
| 28. #15667941 | C22 | semidirect |
| 29. #15667937 | C22 | semidirect |
| 30. #15667933 | C22 | semidirect |
| 31. #15667933 | C22 | semidirect |
| 33. #15667924 | C22 | semidirect |
| 34. C8×Dic89 | C22 | semidirect |
| 76. D8×C89 | D4 | semidirect |
| 123. C22×C89 | #135 | semidirect |
| 144. C89 | #3280 | semidirect |
| 146. C22×D8 | D89 | semidirect |
| 206. D8 | C22⋊D89 | semidirect |
| 270. C22 | #15668031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668031 | 2 |
| #19152242 | 2 |
| #19151981 | 2 |
| #19151839 | 2 |
| #19151831 | 2 |
| #19151811 | 2 |
| #19151749 | 2 |
| #19151740 | 2 |
| D8×Dic89 | 2 |
| C8×C22⋊D89 | 2 |
| C22×D8×C89 | 2 |
| #3280 | 89 |