Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. #26020975 | C2 | semidirect |
| 2. #26018909 | C2 | semidirect |
| 4. #26018751 | C2 | semidirect |
| 6. #26018083 | C2 | semidirect |
| 196. C89 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020975 | 2 |
| #26018909 | 2 |
| #26018901 | 2 |
| #26018751 | 2 |
| #26018747 | 2 |
| #26018083 | 2 |
| C89×#3135 | 2 |
| #10547 | 89 |