Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 101. C4×Dic89 | Q16 | semidirect |
| 201. C89 | #10017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030287 | 2 |
| #26023543 | 2 |
| #26021234 | 2 |
| #26018682 | 2 |
| #26018681 | 2 |
| #26018080 | 2 |
| C89×#3104 | 2 |
| #10017 | 89 |