Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
590 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26030648 | C2 | semidirect |
| 3. #26026364 | C2 | semidirect |
| 4. #26018851 | C2 | semidirect |
| 5. #26018761 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1556 | C2 | semidirect |
| 196. #1556 | D89 | semidirect |
| 200. C89 | #10094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031241 | 2 |
| #26030648 | 2 |
| #26026364 | 2 |
| #26018851 | 2 |
| #26018761 | 2 |
| #26018144 | 2 |
| C89×#1556 | 2 |
| #10094 | 89 |