Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
728 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #26021907 | C2 | semidirect |
| 3. #26020802 | C2 | semidirect |
| 8. #19152348 | C4 | semidirect |
| 9. #19152334 | C4 | semidirect |
| 197. C89 | #12771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034666 | 2 |
| #26021907 | 2 |
| #26020802 | 2 |
| #26020636 | 2 |
| C89×#2132 | 2 |
| #12771 | 89 |