Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1054 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 10. C4×#13083564 | C4 | semidirect |
| 56. #13083564 | C42 | semidirect |
| 123. C89 | #20507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#13083564 | 2 |
| #26022615 | 2 |
| C4×#15667945 | 2 |
| #26020085 | 2 |
| #26020082 | 2 |
| #26019939 | 2 |
| C89×#2276 | 2 |
| #20507 | 89 |