Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19151994 | C4 | semidirect |
| 10. #19151948 | C4 | semidirect |
| 170. C89 | #9292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031393 | 2 |
| #26029193 | 2 |
| #26021071 | 2 |
| #26018923 | 2 |
| #26018110 | 2 |
| #26018082 | 2 |
| C89×#1518 | 2 |
| #9292 | 89 |