Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
644 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 644 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. #26018829 | C2 | semidirect |
| 2. #26018660 | C2 | semidirect |
| 10. #564×C89 | C4 | semidirect |
| 11. #562×C89 | C4 | semidirect |
| 121. C89 | #8515 | semidirect |
| 122. #564 | Dic89 | semidirect |
| 123. #562 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018829 | 2 |
| #26018660 | 2 |
| C89×#3567 | 2 |
| #8515 | 89 |