Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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. #19152172 | C2 | semidirect |
| 3. #19151787 | C2 | semidirect |
| 4. #19151572 | C2 | semidirect |
| 5. #19151571 | C2 | semidirect |
| 6. #536×C89 | C2 | semidirect |
| 17. #15667995 | C22 | semidirect |
| 19. #15667971 | C22 | semidirect |
| 20. #15667927 | C22 | semidirect |
| 21. #15667926 | C22 | semidirect |
| 23. C22×Q8×C89 | C22 | semidirect |
| 26. #123×C89 | C22 | semidirect |
| 28. #117×C89 | C22 | semidirect |
| 129. C89 | #3028 | semidirect |
| 132. #536 | D89 | semidirect |
| 145. C22×Q8 | C2×D89 | semidirect |
| 151. #123 | C2×D89 | semidirect |
| 155. #117 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152434 | 2 |
| #19152172 | 2 |
| #19151787 | 2 |
| #19151572 | 2 |
| #19151571 | 2 |
| #536×C89 | 2 |
| #3028 | 89 |