Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
238 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 9. #19151349 | C4 | semidirect |
| 11. C4⋊C16×C89 | C4 | semidirect |
| 88. C89 | #7302 | semidirect |
| 93. C4⋊C16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667944 | 2 |
| #26019008 | 2 |
| C89×#2163 | 2 |
| #7302 | 89 |