Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 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 |
|---|---|---|
| 57. Q16×C89 | Q16 | semidirect |
| 108. C89 | #12446 | semidirect |
| 151. Q16 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022394 | 2 |
| #26019869 | 2 |
| Q16×#10623494 | 2 |
| #26018321 | 2 |
| #26018307 | 2 |
| #26018306 | 2 |
| C89×#2225 | 2 |
| #12446 | 89 |