Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 20. #19151392 | C4 | semidirect |
| 76. C2×Dic178 | C4⋊C4 | semidirect |
| 101. C4×Dic89 | C4⋊C4 | semidirect |
| 237. C89 | #12967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023422 | 2 |
| C2×#19151392 | 2 |
| #26020640 | 2 |
| #26020533 | 2 |
| #26018370 | 2 |
| #26018369 | 2 |
| C89×#1867 | 2 |
| #12967 | 89 |