Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26018983 | C2 | semidirect |
| 4. #26018765 | C2 | semidirect |
| 7. #19152334 | C4 | semidirect |
| 8. #19152328 | C4 | semidirect |
| 148. C89 | #8492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034666 | 2 |
| #26021085 | 2 |
| #26018983 | 2 |
| #26018765 | 2 |
| C89×#1536 | 2 |
| #8492 | 89 |