Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26019160 | C2 | semidirect |
| 4. #26018221 | C2 | semidirect |
| 6. #26018172 | C2 | semidirect |
| 7. C89×#1368 | C2 | semidirect |
| 66. C16×C89 | M16 | semidirect |
| 106. #1368 | D89 | semidirect |
| 110. C89 | #12087 | semidirect |
| 169. C16 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022118 | 2 |
| #26019165 | 2 |
| #26019160 | 2 |
| #26018221 | 2 |
| #26018218 | 2 |
| #26018172 | 2 |
| C89×#1368 | 2 |
| #12087 | 89 |