Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26020300 | C2 | semidirect |
| 4. #26018375 | C2 | semidirect |
| 5. C89×#1392 | C2 | semidirect |
| 146. #1392 | D89 | semidirect |
| 147. C89 | #12809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028960 | 2 |
| #26021935 | 2 |
| #26020300 | 2 |
| #26018375 | 2 |
| C89×#1392 | 2 |
| #12809 | 89 |