Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #26033355 | C2 | semidirect |
| 3. #26021987 | C2 | semidirect |
| 4. #26018357 | C2 | semidirect |
| 5. C89×#1812 | C2 | semidirect |
| 11. #19151856 | C4 | semidirect |
| 12. #19151851 | C4 | semidirect |
| 35. #15667952 | D4 | semidirect |
| 142. #1812 | D89 | semidirect |
| 144. C89 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033355 | 2 |
| #26029914 | 2 |
| #26021987 | 2 |
| #26018357 | 2 |
| C89×#1812 | 2 |
| #13077 | 89 |