Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
758 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 758 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. #26021941 | C2 | semidirect |
| 2. C2×#19151395 | C2 | semidirect |
| 3. #26020790 | C2 | semidirect |
| 4. #26020656 | C2 | semidirect |
| 6. #19152076 | C22 | semidirect |
| 9. C2×#15667931 | C22 | semidirect |
| 10. C2×#15667931 | C22 | semidirect |
| 17. #563×C89 | C4 | semidirect |
| 19. H(3,𝔽4)×C89 | C4 | semidirect |
| 20. #555×C89 | C4 | semidirect |
| 247. C89 | #12781 | semidirect |
| 248. #563 | Dic89 | semidirect |
| 250. H(3,𝔽4) | Dic89 | semidirect |
| 251. #555 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021941 | 2 |
| C2×#19151395 | 2 |
| #26020790 | 2 |
| #26020656 | 2 |
| C89×#3545 | 2 |
| #12781 | 89 |