Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#19151376 | C2 | semidirect |
| 4. #26018331 | C2 | semidirect |
| 5. C2×#347×C89 | C2 | semidirect |
| 15. #19151377 | C4 | semidirect |
| 136. C2×#347 | D89 | semidirect |
| 138. C89 | #12606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151555 | 2 |
| #26021862 | 2 |
| C2×#19151376 | 2 |
| #26018331 | 2 |
| C2×#347×C89 | 2 |
| #12606 | 89 |