Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C2×#15668041 | C2 | semidirect |
| 3. C22⋊Q8×D89 | C2 | semidirect |
| 4. #19151761 | C2 | semidirect |
| 5. #19151757 | C2 | semidirect |
| 6. #19151756 | C2 | semidirect |
| 7. #19151753 | C2 | semidirect |
| 8. #19151749 | C2 | semidirect |
| 9. #19151596 | C2 | semidirect |
| 10. #19151560 | C2 | semidirect |
| 11. #450×C89 | C2 | semidirect |
| 18. C2×Q8×D89 | C22 | semidirect |
| 23. C2×Dic356 | C22 | semidirect |
| 24. C2×#13083564 | C22 | semidirect |
| 25. C2×#13083562 | C22 | semidirect |
| 26. C2×#13083557 | C22 | semidirect |
| 27. #15667992 | C22 | semidirect |
| 31. #15667988 | C22 | semidirect |
| 33. C4⋊C4×D89 | C22 | semidirect |
| 35. #15667937 | C22 | semidirect |
| 36. #15667935 | C22 | semidirect |
| 37. #15667933 | C22 | semidirect |
| 39. #15667924 | C22 | semidirect |
| 41. C2×SD16×C89 | C22 | semidirect |
| 43. #102×C89 | C22 | semidirect |
| 146. C22×C89 | #137 | semidirect |
| 172. C89 | #3007 | semidirect |
| 181. #450 | D89 | semidirect |
| 199. C2×SD16 | C2×D89 | semidirect |
| 213. #102 | C2×D89 | semidirect |
| 325. C22 | #15668041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083573 | 2 |
| C2×#15668041 | 2 |
| C22⋊Q8×D89 | 2 |
| #19151761 | 2 |
| #19151757 | 2 |
| #19151756 | 2 |
| #19151753 | 2 |
| #19151749 | 2 |
| #19151596 | 2 |
| #19151560 | 2 |
| #450×C89 | 2 |
| #3007 | 89 |