Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #19152321 | C2 | semidirect |
| 2. #19151955 | C2 | semidirect |
| 3. #19151950 | C2 | semidirect |
| 4. #19151902 | C2 | semidirect |
| 5. #19151885 | C2 | semidirect |
| 7. #19151803 | C2 | semidirect |
| 8. Q8×#10623494 | C2 | semidirect |
| 9. C4×#13083562 | C2 | semidirect |
| 11. #554×C89 | C2 | semidirect |
| 121. C89 | #3360 | semidirect |
| 123. #554 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152321 | 2 |
| #19151955 | 2 |
| #19151950 | 2 |
| #19151902 | 2 |
| #19151885 | 2 |
| #19151813 | 2 |
| #19151803 | 2 |
| Q8×#10623494 | 2 |
| C4×#13083562 | 2 |
| C4×#13083559 | 2 |
| #554×C89 | 2 |
| #3360 | 89 |