Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #19152153 | C2 | semidirect |
| 3. #19151904 | C2 | semidirect |
| 4. #19151896 | C2 | semidirect |
| 5. #19151894 | C2 | semidirect |
| 6. #19151888 | C2 | semidirect |
| 7. #19151880 | C2 | semidirect |
| 8. #19151635 | C2 | semidirect |
| 9. C4⋊C8×D89 | C2 | semidirect |
| 11. #474×C89 | C2 | semidirect |
| 44. #13083573 | Q8 | semidirect |
| 135. C89 | #3076 | semidirect |
| 143. #474 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152153 | 2 |
| C4×#13083573 | 2 |
| #19151904 | 2 |
| #19151896 | 2 |
| #19151894 | 2 |
| #19151888 | 2 |
| #19151880 | 2 |
| #19151635 | 2 |
| C4⋊C8×D89 | 2 |
| #19151591 | 2 |
| #474×C89 | 2 |
| #3076 | 89 |