Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 138. C89 | #8705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151465 | 2 |
| #26020318 | 2 |
| #26018095 | 2 |
| #26018094 | 2 |
| C89×#1280 | 2 |
| #8705 | 89 |