Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
206 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 206 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 |
|---|---|---|
| 54. #13083549 | Q16 | semidirect |
| 105. C89 | #12054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022161 | 2 |
| #26022157 | 2 |
| C8×#13083564 | 2 |
| #26018321 | 2 |
| #26018232 | 2 |
| C16×#10623494 | 2 |
| C89×Q8⋊C16 | 2 |
| #12054 | 89 |