Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
226 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 18. Dic712 | C8 | direct (N × H) |
| 56. C8×C89 | Q32 | semidirect |
| 77. C89 | C8×Q32 | semidirect |
| 129. C8 | Dic712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic712 | 2 |
| C8×Dic356 | 2 |
| #26018324 | 2 |
| #26018217 | 2 |
| C8×C16×C89 | 2 |
| C8×Q32 | 89 |