Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 91. Q8×C89 | Q32 | semidirect |
| 133. C89 | #12334 | semidirect |
| 221. Q8 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033258 | 2 |
| #26022504 | 2 |
| #26022299 | 2 |
| #26018300 | 2 |
| Q8⋊#13083549 | 2 |
| #26018215 | 2 |
| C89×#1670 | 2 |
| #12334 | 89 |