Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
878 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 878 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×#19151391 | C2 | semidirect |
| 2. #26021898 | C2 | semidirect |
| 3. #26020795 | C2 | semidirect |
| 4. #26020651 | C2 | semidirect |
| 6. #19152073 | C22 | semidirect |
| 8. C2×#15667929 | C22 | semidirect |
| 10. C2×#15667927 | C22 | semidirect |
| 18. #560×C89 | C4 | semidirect |
| 19. #559×C89 | C4 | semidirect |
| 23. D42×C89 | C4 | semidirect |
| 269. C89 | #12767 | semidirect |
| 271. #560 | Dic89 | semidirect |
| 272. #559 | Dic89 | semidirect |
| 276. D42 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26021898 | 2 |
| #26020795 | 2 |
| #26020651 | 2 |
| C89×#3543 | 2 |
| #12767 | 89 |