Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26021917 | C2 | semidirect |
| 2. #26018415 | C2 | semidirect |
| 6. #19151391 | C22 | semidirect |
| 9. C2×#127×C89 | C4 | semidirect |
| 12. #492×C89 | C4 | semidirect |
| 13. C4×M16×C89 | C4 | semidirect |
| 114. C89 | #13585 | semidirect |
| 117. C2×#127 | Dic89 | semidirect |
| 120. #492 | Dic89 | semidirect |
| 122. C4×M16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26018415 | 2 |
| C89×#3151 | 2 |
| #13585 | 89 |