Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 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 |
|---|---|---|
| 1. C22×#13083573 | C2 | semidirect |
| 2. C2×#15668033 | C2 | semidirect |
| 3. #19152111 | C2 | semidirect |
| 4. #19151757 | C2 | semidirect |
| 5. #19151753 | C2 | semidirect |
| 6. #19151744 | C2 | semidirect |
| 7. #19151739 | C2 | semidirect |
| 8. #19151732 | C2 | semidirect |
| 9. #19151591 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #450×C89 | C2 | semidirect |
| 12. C2×#13083575 | C22 | semidirect |
| 23. C2×#13083564 | C22 | semidirect |
| 24. C2×#13083563 | C22 | semidirect |
| 25. C2×#13083559 | C22 | semidirect |
| 26. C2×C8×D89 | C22 | semidirect |
| 28. #15667988 | C22 | semidirect |
| 29. #15667987 | C22 | semidirect |
| 34. #15667970 | 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 |
| 52. #13083573 | D4 | semidirect |
| 147. C22×C89 | #135 | semidirect |
| 176. C89 | #3002 | semidirect |
| 182. #450 | D89 | semidirect |
| 202. C2×SD16 | C2×D89 | semidirect |
| 217. #102 | C2×D89 | semidirect |
| 333. C22 | #15668033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083573 | 2 |
| C2×#15668033 | 2 |
| #19152111 | 2 |
| #19151757 | 2 |
| #19151753 | 2 |
| #19151744 | 2 |
| #19151739 | 2 |
| #19151732 | 2 |
| #19151591 | 2 |
| C22⋊C8×D89 | 2 |
| #450×C89 | 2 |
| #3002 | 89 |