Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #19151990 | C2 | semidirect |
| 3. #19151960 | C2 | semidirect |
| 4. #19151820 | C2 | semidirect |
| 5. #19151753 | C2 | semidirect |
| 7. #19151655 | C2 | semidirect |
| 8. #533×C89 | C2 | semidirect |
| 11. C2×#13083564 | C22 | semidirect |
| 19. C4⋊#10623494 | C22 | semidirect |
| 20. #15667935 | C22 | semidirect |
| 23. #15667923 | C22 | semidirect |
| 24. C4⋊Q8×C89 | C22 | semidirect |
| 25. C4⋊Q8×C89 | C22 | semidirect |
| 30. C4×Q8×C89 | C22 | semidirect |
| 113. C89 | #3215 | semidirect |
| 114. #533 | D89 | semidirect |
| 126. C4⋊Q8 | C2×D89 | semidirect |
| 127. C4⋊Q8 | C2×D89 | semidirect |
| 136. C4×Q8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668000 | 2 |
| #19151990 | 2 |
| #19151960 | 2 |
| #19151820 | 2 |
| #19151753 | 2 |
| #19151748 | 2 |
| #19151655 | 2 |
| #533×C89 | 2 |
| #3215 | 89 |