Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 80. #13083558 | Q16 | semidirect |
| 185. C89 | #10199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031594 | 2 |
| #26030794 | 2 |
| #26021201 | 2 |
| #26021197 | 2 |
| #26018752 | 2 |
| #26018101 | 2 |
| C89×#3209 | 2 |
| #10199 | 89 |