Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19151990 | C2 | semidirect |
| 3. #19151972 | C2 | semidirect |
| 4. #19151964 | C2 | semidirect |
| 5. #19151955 | C2 | semidirect |
| 6. #19151820 | C2 | semidirect |
| 7. #19151798 | C2 | semidirect |
| 8. #19151758 | C2 | semidirect |
| 9. #19151748 | C2 | semidirect |
| 10. #19151659 | C2 | semidirect |
| 11. #541×C89 | C2 | semidirect |
| 14. C2×#13083564 | C22 | semidirect |
| 17. C2×#13083561 | C22 | semidirect |
| 24. C4⋊#10623494 | C22 | semidirect |
| 25. #15667935 | C22 | semidirect |
| 28. #15667932 | C22 | semidirect |
| 30. #15667923 | C22 | semidirect |
| 31. C4×#10623494 | C22 | semidirect |
| 32. C4⋊Q8×C89 | C22 | semidirect |
| 35. #125×C89 | C22 | semidirect |
| 37. C4×Q8×C89 | C22 | semidirect |
| 123. C89 | #3222 | semidirect |
| 124. #541 | D89 | semidirect |
| 141. C4⋊Q8 | C2×D89 | semidirect |
| 146. #125 | C2×D89 | semidirect |
| 152. C4×Q8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152167 | 2 |
| #19151990 | 2 |
| #19151972 | 2 |
| #19151964 | 2 |
| #19151955 | 2 |
| #19151820 | 2 |
| #19151798 | 2 |
| #19151758 | 2 |
| #19151748 | 2 |
| #19151659 | 2 |
| #541×C89 | 2 |
| #3222 | 89 |