Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
856 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26021937 | C2 | semidirect |
| 2. #26021902 | C2 | semidirect |
| 3. #26020800 | C2 | semidirect |
| 4. #26020636 | C2 | semidirect |
| 6. #19152365 | C22 | semidirect |
| 8. #19151582 | C22 | semidirect |
| 10. #19151572 | C22 | semidirect |
| 17. H(3,𝔽4)×C89 | C4 | semidirect |
| 21. D42×C89 | C4 | semidirect |
| 212. C89 | #12769 | semidirect |
| 215. H(3,𝔽4) | Dic89 | semidirect |
| 219. D42 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021937 | 2 |
| #26021902 | 2 |
| #26020800 | 2 |
| #26020636 | 2 |
| C89×#3549 | 2 |
| #12769 | 89 |