Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
676 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. C2×#19151397 | C2 | semidirect |
| 5. #26018378 | C2 | semidirect |
| 6. #26018378 | C2 | semidirect |
| 7. C2×#356×C89 | C2 | semidirect |
| 251. C2×D89 | #356 | semidirect |
| 276. C2×#356 | D89 | semidirect |
| 280. C89 | #13094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#101×D89 | 2 |
| #26023893 | 2 |
| C2×#19151397 | 2 |
| #26020174 | 2 |
| #26018378 | 2 |
| C2×#356×C89 | 2 |
| #13094 | 89 |