Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152334 | C2 | semidirect |
| 2. #19152322 | C2 | semidirect |
| 3. #19151979 | C2 | semidirect |
| 4. #19151818 | C2 | semidirect |
| 5. #19151815 | C2 | semidirect |
| 6. #19151805 | C2 | semidirect |
| 8. C8×Dic178 | C2 | semidirect |
| 9. C4×#13083563 | C2 | semidirect |
| 10. SD16×Dic89 | C2 | semidirect |
| 11. #492×C89 | C2 | semidirect |
| 126. C89 | #3394 | semidirect |
| 130. #492 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152334 | 2 |
| #19152322 | 2 |
| #19151979 | 2 |
| #19151818 | 2 |
| #19151815 | 2 |
| #19151805 | 2 |
| #19151790 | 2 |
| C8×Dic178 | 2 |
| C4×#13083563 | 2 |
| SD16×Dic89 | 2 |
| #492×C89 | 2 |
| #3394 | 89 |