Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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. #19152210 | C2 | semidirect |
| 3. #19151940 | C2 | semidirect |
| 4. #19151899 | C2 | semidirect |
| 5. #19151804 | C2 | semidirect |
| 7. #19151700 | C2 | semidirect |
| 8. C4×#13083563 | C2 | semidirect |
| 9. #433×C89 | C2 | semidirect |
| 13. #15668012 | C22 | semidirect |
| 15. #15668004 | C22 | semidirect |
| 18. C4×Dic178 | C22 | semidirect |
| 24. #15667946 | C22 | semidirect |
| 25. #15667944 | C22 | semidirect |
| 26. #15667937 | C22 | semidirect |
| 27. #15667937 | C22 | semidirect |
| 31. C4⋊C8×C89 | C22 | semidirect |
| 33. #97×C89 | C22 | semidirect |
| 34. C4×C8×C89 | C22 | semidirect |
| 103. C89 | #3123 | semidirect |
| 112. #433 | D89 | semidirect |
| 130. C4⋊C8 | C2×D89 | semidirect |
| 136. #97 | C2×D89 | semidirect |
| 137. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152210 | 2 |
| #19152072 | 2 |
| #19151940 | 2 |
| #19151899 | 2 |
| #19151804 | 2 |
| #19151751 | 2 |
| #19151700 | 2 |
| C4×#13083563 | 2 |
| #433×C89 | 2 |
| #3123 | 89 |