Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
246 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 53. #13083549 | Q16 | semidirect |
| 63. C16×C89 | Q16 | semidirect |
| 99. C89 | #12524 | semidirect |
| 155. C16 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022532 | 2 |
| #26022527 | 2 |
| #26022525 | 2 |
| #26019869 | 2 |
| #26019861 | 2 |
| #26018168 | 2 |
| C89×#2254 | 2 |
| #12524 | 89 |