Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 5. C2×#15667944 | C4 | semidirect |
| 9. #19151361 | C4 | semidirect |
| 13. C22⋊C16×C89 | C4 | semidirect |
| 119. C89 | #7262 | semidirect |
| 126. C22⋊C16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020277 | 2 |
| #26019969 | 2 |
| C89×#2112 | 2 |
| #7262 | 89 |