Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26018969 | C2 | semidirect |
| 5. #26018764 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#3165 | C2 | semidirect |
| 186. #3165 | D89 | semidirect |
| 192. C89 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031251 | 2 |
| #26026364 | 2 |
| #26018969 | 2 |
| #26018849 | 2 |
| #26018764 | 2 |
| #26018146 | 2 |
| C89×#3165 | 2 |
| #10102 | 89 |