Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #26020975 | C2 | semidirect |
| 3. #26018899 | C2 | semidirect |
| 4. #26018748 | C2 | semidirect |
| 5. C89×#1275 | C2 | semidirect |
| 154. #1275 | D89 | semidirect |
| 155. C89 | #10546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030698 | 2 |
| #26020975 | 2 |
| #26018899 | 2 |
| #26018748 | 2 |
| C89×#1275 | 2 |
| #10546 | 89 |