Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#15668039 | C2 | semidirect |
| 2. #19152241 | C2 | semidirect |
| 3. #19151841 | C2 | semidirect |
| 4. #19151810 | C2 | semidirect |
| 5. #19151759 | C2 | semidirect |
| 6. #19151730 | C2 | semidirect |
| 7. C4×D712 | C2 | semidirect |
| 8. #19151677 | C2 | semidirect |
| 9. #495×C89 | C2 | semidirect |
| 11. C2×D4×D89 | C22 | semidirect |
| 13. C2×#13083561 | C22 | semidirect |
| 16. C2×#13083557 | C22 | semidirect |
| 18. #15667988 | C22 | semidirect |
| 23. C4×D356 | C22 | semidirect |
| 25. #15667946 | C22 | semidirect |
| 26. C4⋊#10623494 | C22 | semidirect |
| 27. #15667936 | C22 | semidirect |
| 28. #15667934 | C22 | semidirect |
| 29. #15667933 | C22 | semidirect |
| 30. #15667924 | C22 | semidirect |
| 31. C2×Q16×C89 | C22 | semidirect |
| 32. C2×SD16×C89 | C22 | semidirect |
| 34. #124×C89 | C22 | semidirect |
| 35. C4×C8×C89 | C22 | semidirect |
| 50. D712 | D4 | semidirect |
| 125. C89 | #3273 | semidirect |
| 128. #495 | D89 | semidirect |
| 138. C2×Q16 | C2×D89 | semidirect |
| 140. C2×SD16 | C2×D89 | semidirect |
| 145. #124 | C2×D89 | semidirect |
| 160. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668039 | 2 |
| #19152241 | 2 |
| #19151841 | 2 |
| #19151810 | 2 |
| #19151759 | 2 |
| #19151730 | 2 |
| C4×D712 | 2 |
| #19151677 | 2 |
| #495×C89 | 2 |
| #3273 | 89 |