Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152314 | C2 | semidirect |
| 2. D4×D356 | C2 | semidirect |
| 3. #19151946 | C2 | semidirect |
| 4. #19151924 | C2 | semidirect |
| 5. #19151852 | C2 | semidirect |
| 6. #19151794 | C2 | semidirect |
| 7. #19151733 | C2 | semidirect |
| 8. C4×#13083559 | C2 | semidirect |
| 9. #19151675 | C2 | semidirect |
| 10. #19151601 | C2 | semidirect |
| 11. #476×C89 | C2 | semidirect |
| 14. C2×D712 | C22 | semidirect |
| 16. C2×#13083557 | C22 | semidirect |
| 21. #15667987 | C22 | semidirect |
| 25. C4×D356 | C22 | semidirect |
| 27. #15667970 | C22 | semidirect |
| 28. #15667945 | C22 | semidirect |
| 29. #15667934 | C22 | semidirect |
| 31. #15667932 | C22 | semidirect |
| 32. #15667932 | C22 | semidirect |
| 33. #15667932 | C22 | semidirect |
| 34. #15667924 | C22 | semidirect |
| 35. C4×#10623494 | C22 | semidirect |
| 36. C4⋊Q8×C89 | C22 | semidirect |
| 38. #106×C89 | C22 | semidirect |
| 39. C4⋊C8×C89 | C22 | semidirect |
| 141. C89 | #3325 | semidirect |
| 146. #476 | D89 | semidirect |
| 158. C4⋊Q8 | C2×D89 | semidirect |
| 172. #106 | C2×D89 | semidirect |
| 173. C4⋊C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152314 | 2 |
| D4×D356 | 2 |
| #19151946 | 2 |
| #19151924 | 2 |
| #19151852 | 2 |
| #19151794 | 2 |
| #19151733 | 2 |
| C4×#13083559 | 2 |
| #19151675 | 2 |
| #19151601 | 2 |
| #476×C89 | 2 |
| #3325 | 89 |