Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 1. #26031375 | C2 | semidirect |
| 3. #26021072 | C2 | semidirect |
| 4. #26018813 | C2 | semidirect |
| 5. C89×#1281 | C2 | semidirect |
| 132. #1281 | D89 | semidirect |
| 133. C89 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031375 | 2 |
| #26030698 | 2 |
| #26021072 | 2 |
| #26018813 | 2 |
| C89×#1281 | 2 |
| #10225 | 89 |