Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 82. Dic178 | Q32 | semidirect |
| 110. C89 | #12440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022504 | 2 |
| #26022154 | 2 |
| #26019623 | 2 |
| #26019619 | 2 |
| #26018323 | 2 |
| #26018302 | 2 |
| C89×#1362 | 2 |
| #12440 | 89 |