Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#19151437 | C2 | semidirect |
| 2. #26022343 | C2 | semidirect |
| 4. #26018452 | C2 | semidirect |
| 5. #26018434 | C2 | semidirect |
| 6. #26018431 | C2 | semidirect |
| 7. C2×M64×C89 | C2 | semidirect |
| 39. C32×C89 | D4 | semidirect |
| 97. C2×M64 | D89 | semidirect |
| 103. C89 | #13699 | semidirect |
| 135. C32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151437 | 2 |
| #26022343 | 2 |
| #26022338 | 2 |
| #26018452 | 2 |
| #26018434 | 2 |
| #26018431 | 2 |
| C2×M64×C89 | 2 |
| #13699 | 89 |