Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
300 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #26018232 | C2 | semidirect |
| 113. C89 | #11638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029186 | 2 |
| #26022051 | 2 |
| #26018232 | 2 |
| C89×#2162 | 2 |
| #11638 | 89 |