Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19151376 | C2 | semidirect |
| 3. #26018286 | C2 | semidirect |
| 4. #26018284 | C2 | semidirect |
| 5. C2×#347×C89 | C2 | semidirect |
| 141. C2×#347 | D89 | semidirect |
| 144. C89 | #11911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030598 | 2 |
| C2×#19151376 | 2 |
| #26018286 | 2 |
| #26018284 | 2 |
| C2×#347×C89 | 2 |
| #11911 | 89 |