Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D89 | C2 | semidirect |
| 2. C2×#15668041 | C2 | semidirect |
| 4. #19151756 | C2 | semidirect |
| 5. #19151755 | C2 | semidirect |
| 6. #19151754 | C2 | semidirect |
| 7. #19151736 | C2 | semidirect |
| 8. #19151735 | C2 | semidirect |
| 9. #19151605 | C2 | semidirect |
| 10. #19151560 | C2 | semidirect |
| 11. #448×C89 | C2 | semidirect |
| 23. C2×Dic356 | C22 | semidirect |
| 24. C2×#13083564 | C22 | semidirect |
| 25. C2×#13083562 | C22 | semidirect |
| 35. #15667937 | C22 | semidirect |
| 36. #15667936 | C22 | semidirect |
| 37. #15667935 | C22 | semidirect |
| 41. C2×SD16×C89 | C22 | semidirect |
| 43. #103×C89 | C22 | semidirect |
| 59. Q8×D89 | D4 | semidirect |
| 144. C22×C89 | #137 | semidirect |
| 152. C2×D89 | #137 | semidirect |
| 170. C89 | #3004 | semidirect |
| 179. #448 | D89 | semidirect |
| 197. C2×SD16 | C2×D89 | semidirect |
| 211. #103 | C2×D89 | semidirect |
| 321. C22 | #15668041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D89 | 2 |
| C2×#15668041 | 2 |
| #19152108 | 2 |
| #19151756 | 2 |
| #19151755 | 2 |
| #19151754 | 2 |
| #19151736 | 2 |
| #19151735 | 2 |
| #19151605 | 2 |
| #19151560 | 2 |
| #448×C89 | 2 |
| #3004 | 89 |