Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26022051 | C2 | semidirect |
| 3. #26018305 | C2 | semidirect |
| 4. #26018294 | C2 | semidirect |
| 5. C2×#334×C89 | C2 | semidirect |
| 140. C2×#334 | D89 | semidirect |
| 143. C89 | #11944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030822 | 2 |
| #26022051 | 2 |
| #26018305 | 2 |
| #26018294 | 2 |
| C2×#334×C89 | 2 |
| #11944 | 89 |