Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
344 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 2. #26022051 | C2 | semidirect |
| 3. #26018311 | C2 | semidirect |
| 4. #26018297 | C2 | semidirect |
| 5. C89×#1564 | C2 | semidirect |
| 122. #1564 | D89 | semidirect |
| 125. C89 | #11948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030831 | 2 |
| #26022051 | 2 |
| #26018311 | 2 |
| #26018297 | 2 |
| C89×#1564 | 2 |
| #11948 | 89 |