Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 74. Q8×C89 | Q32 | semidirect |
| 107. C89 | #33962 | semidirect |
| 176. 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 |
| #26022302 | 2 |
| #26022299 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667958 | 2 |
| C89×#3395 | 2 |
| #33962 | 89 |