Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 2. #26022533 | C2 | direct (N × H) |
| 27. C2×#13083549 | Q8 | semidirect |
| 36. C2×C16×C89 | Q8 | semidirect |
| 51. #13083549 | C2×Q8 | semidirect |
| 60. C16×C89 | C2×Q8 | semidirect |
| 87. C2×C89 | #2254 | semidirect |
| 96. C89 | C2×#2254 | semidirect |
| 121. C2×C16 | Dic178 | semidirect |
| 150. C16 | C2×Dic178 | semidirect |
| 176. C2 | #26022533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152002 | 2 |
| #26022533 | 2 |
| C2×#19151426 | 2 |
| C2×#19151425 | 2 |
| C2×C16×Dic89 | 2 |
| C2×#367×C89 | 2 |
| C2×#2254 | 89 |