Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 44. #13083564 | C16 | direct (N × H) |
| 64. C16×C89 | Q16 | semidirect |
| 105. C89 | C16×Q16 | semidirect |
| 162. C16 | #13083564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic178 | 2 |
| C8×#13083564 | 2 |
| #26018321 | 2 |
| Q8⋊#13083549 | 2 |
| #26018230 | 2 |
| C16×#10623494 | 2 |
| Q8×C16×C89 | 2 |
| C16×Q16 | 89 |