Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 58. C22×Dic89 | Q16 | semidirect |
| 156. C89 | #10325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028586 | 2 |
| #26020318 | 2 |
| #26018824 | 2 |
| #26018120 | 2 |
| C89×#3189 | 2 |
| #10325 | 89 |