Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19151964 | C2 | semidirect |
| 3. #19151960 | C2 | semidirect |
| 4. #19151955 | C2 | semidirect |
| 5. #19151946 | C2 | semidirect |
| 6. #19151602 | C2 | semidirect |
| 7. #19151597 | C2 | semidirect |
| 8. #19151592 | C2 | semidirect |
| 9. C2×#15667932 | C2 | semidirect |
| 10. #19151554 | C2 | semidirect |
| 11. #544×C89 | C2 | semidirect |
| 21. #15667935 | C22 | semidirect |
| 22. #15667935 | C22 | semidirect |
| 23. #15667935 | C22 | semidirect |
| 28. #15667932 | C22 | semidirect |
| 29. #15667932 | C22 | semidirect |
| 30. #15667932 | C22 | semidirect |
| 31. #15667923 | C22 | semidirect |
| 32. C4×#10623494 | C22 | semidirect |
| 34. C4⋊Q8×C89 | C22 | semidirect |
| 36. #125×C89 | C22 | semidirect |
| 136. C89 | #3136 | semidirect |
| 137. #544 | D89 | semidirect |
| 153. C4⋊Q8 | C2×D89 | semidirect |
| 156. #125 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152167 | 2 |
| #19151964 | 2 |
| #19151960 | 2 |
| #19151955 | 2 |
| #19151946 | 2 |
| #19151602 | 2 |
| #19151597 | 2 |
| #19151592 | 2 |
| C2×#15667932 | 2 |
| #19151554 | 2 |
| #544×C89 | 2 |
| #3136 | 89 |