Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
778 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 778 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. C2×#19151393 | C2 | semidirect |
| 2. #26021898 | C2 | semidirect |
| 3. #26020795 | C2 | semidirect |
| 4. #26020641 | C2 | semidirect |
| 17. #563×C89 | C4 | semidirect |
| 19. H(3,𝔽4)×C89 | C4 | semidirect |
| 22. #551×C89 | C4 | semidirect |
| 250. C89 | #12768 | semidirect |
| 251. #563 | Dic89 | semidirect |
| 253. H(3,𝔽4) | Dic89 | semidirect |
| 256. #551 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| #26021898 | 2 |
| #26020795 | 2 |
| #26020641 | 2 |
| C89×#3545 | 2 |
| #12768 | 89 |