Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26018943 | C2 | semidirect |
| 4. #26018708 | C2 | semidirect |
| 6. #26018126 | C2 | semidirect |
| 7. C89×#1566 | C2 | semidirect |
| 184. #1566 | D89 | semidirect |
| 189. C89 | #10460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030051 | 2 |
| #26020241 | 2 |
| #26018943 | 2 |
| #26018708 | 2 |
| C2×#19151327 | 2 |
| #26018126 | 2 |
| C89×#1566 | 2 |
| #10460 | 89 |