Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19151640 | C2 | semidirect |
| 5. #19151463 | C2 | semidirect |
| 6. #19151359 | C2 | semidirect |
| 7. #343×C89 | C2 | semidirect |
| 19. #15667938 | C4 | semidirect |
| 47. C4×Dic89 | C2×C4 | semidirect |
| 53. M16×C89 | C2×C4 | semidirect |
| 112. C89 | #1860 | semidirect |
| 118. #343 | D89 | semidirect |
| 154. M16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152079 | 2 |
| #19151640 | 2 |
| C2×#15667938 | 2 |
| #19151600 | 2 |
| #19151463 | 2 |
| #19151359 | 2 |
| #343×C89 | 2 |
| #1860 | 89 |