Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C2×C22⋊#13083549 | C2 | semidirect |
| 2. #26018194 | C2 | semidirect |
| 3. #26018178 | C2 | semidirect |
| 128. C89 | #11468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13083549 | 2 |
| #26018194 | 2 |
| #26018178 | 2 |
| C89×#2929 | 2 |
| #11468 | 89 |