Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
320 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 139. C89 | #8635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029187 | 2 |
| #26019013 | 2 |
| #26018890 | 2 |
| #26018162 | 2 |
| C89×#1537 | 2 |
| #8635 | 89 |