Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#19151389 | C2 | semidirect |
| 3. C2×#19151387 | C2 | semidirect |
| 5. #26020242 | C2 | semidirect |
| 6. #99×Dic89 | C2 | semidirect |
| 10. C22×C22⋊Dic89 | C4 | semidirect |
| 18. #19151459 | C4 | semidirect |
| 19. #19151456 | C4 | semidirect |
| 20. #19151454 | C4 | semidirect |
| 284. C89 | #13222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025139 | 2 |
| C2×#19151389 | 2 |
| C2×#19151387 | 2 |
| C2×#19151385 | 2 |
| #26020242 | 2 |
| #99×Dic89 | 2 |
| C2×AΣL(1,𝔽16)×C89 | 2 |
| #13222 | 89 |