Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. #19151933 | C2 | semidirect |
| 3. #19151931 | C2 | semidirect |
| 4. #19151837 | C2 | semidirect |
| 5. #19151754 | C2 | semidirect |
| 6. #19151753 | C2 | semidirect |
| 10. C2×#13083564 | C22 | semidirect |
| 19. #15667945 | C22 | semidirect |
| 20. #15667936 | C22 | semidirect |
| 21. #15667935 | C22 | semidirect |
| 68. C23×C89 | Q16 | semidirect |
| 121. C89 | #3189 | semidirect |
| 189. C23 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667991 | 2 |
| #19151933 | 2 |
| #19151931 | 2 |
| #19151837 | 2 |
| #19151754 | 2 |
| #19151753 | 2 |
| C2×C22⋊#10623494 | 2 |
| C2×C22⋊Q8×C89 | 2 |
| #3189 | 89 |