Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
186 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022134 | C2 | semidirect |
| 3. #26018456 | C2 | semidirect |
| 4. #26018437 | C2 | semidirect |
| 5. C4×C32×C89 | C2 | semidirect |
| 8. Dic1424 | C4 | semidirect |
| 9. #19151437 | C4 | semidirect |
| 10. D2848 | C4 | semidirect |
| 67. C4×C32 | D89 | semidirect |
| 68. C89 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022561 | 2 |
| #26022134 | 2 |
| #26018456 | 2 |
| #26018437 | 2 |
| C4×C32×C89 | 2 |
| #13655 | 89 |