Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
400 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26018544 | C2 | semidirect |
| 3. #26018535 | C2 | semidirect |
| 4. #26018097 | C2 | semidirect |
| 113. C89 | #8158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018566 | 2 |
| #26018544 | 2 |
| #26018535 | 2 |
| #26018097 | 2 |
| C2×#433×C89 | 2 |
| #8158 | 89 |