Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1220 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 311 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. #26028716 | C2 | semidirect |
| 2. #26021924 | C2 | semidirect |
| 3. #26021917 | C2 | semidirect |
| 7. #19151572 | C22 | semidirect |
| 8. #19151393 | C22 | semidirect |
| 9. #19151391 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C89 | C4 | semidirect |
| 14. #536×C89 | C4 | semidirect |
| 17. C2×#124×C89 | C4 | semidirect |
| 18. C4×#41×C89 | C4 | semidirect |
| 142. C89 | #33362 | semidirect |
| 144. C2×H(5,𝔽2) | Dic89 | semidirect |
| 147. #536 | Dic89 | semidirect |
| 150. C2×#124 | Dic89 | semidirect |
| 152. C4×#41 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028716 | 2 |
| #26021924 | 2 |
| #26021917 | 2 |
| C89×#3500 | 2 |
| #33362 | 89 |