Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
724 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19151392 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 6. C2×#15668010 | C4 | semidirect |
| 8. C2×#15667991 | C4 | semidirect |
| 13. #19151505 | C4 | semidirect |
| 18. C4×C22⋊Dic89 | C4 | semidirect |
| 250. C89 | #13091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023876 | 2 |
| C2×#19151392 | 2 |
| #26020170 | 2 |
| #26018376 | 2 |
| C2×#410×C89 | 2 |
| #13091 | 89 |