Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #26018163 | C2 | semidirect |
| 5. #26018122 | C2 | semidirect |
| 6. #26018114 | C2 | semidirect |
| 7. C89×#1571 | C2 | semidirect |
| 121. #1571 | D89 | semidirect |
| 128. C89 | #10645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018972 | 2 |
| #26018945 | 2 |
| #26018722 | 2 |
| #26018163 | 2 |
| #26018122 | 2 |
| #26018114 | 2 |
| C89×#1571 | 2 |
| #10645 | 89 |