Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
430 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 9. C2×Dic712 | C4 | semidirect |
| 116. C89 | #13240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic712 | 2 |
| C2×#19151401 | 2 |
| C2×#19151373 | 2 |
| #26021111 | 2 |
| C2×#367×C89 | 2 |
| #13240 | 89 |