Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021242 | C2 | semidirect |
| 2. #26021201 | C2 | semidirect |
| 4. #26019005 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 189. C89 | #10502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021242 | 2 |
| #26021201 | 2 |
| #26021172 | 2 |
| #26019005 | 2 |
| #26018929 | 2 |
| #26018154 | 2 |
| C89×#3227 | 2 |
| #10502 | 89 |