Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26020390 | C2 | semidirect |
| 4. #26018127 | C2 | semidirect |
| 5. C2×#334×C89 | C2 | semidirect |
| 136. C2×#334 | D89 | semidirect |
| 139. C89 | #8686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028965 | 2 |
| #26020390 | 2 |
| #26018927 | 2 |
| #26018127 | 2 |
| C2×#334×C89 | 2 |
| #8686 | 89 |