Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
282 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 14. #19151426 | C4 | semidirect |
| 15. #19151424 | C4 | semidirect |
| 78. C16×C89 | C4⋊C4 | semidirect |
| 130. C89 | #13174 | semidirect |
| 201. C16 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022040 | 2 |
| C2×#19151421 | 2 |
| #26021005 | 2 |
| #26020990 | 2 |
| #26018361 | 2 |
| #26018358 | 2 |
| C2×#347×C89 | 2 |
| #13174 | 89 |