Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 84. #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 |
| #26031202 | 2 |
| #26030799 | 2 |
| #26021200 | 2 |
| #26021195 | 2 |
| #26018101 | 2 |
| C89×#1503 | 2 |
| #10199 | 89 |