Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26033388 | C2 | semidirect |
| 2. #26022565 | C2 | semidirect |
| 3. #26018438 | C2 | semidirect |
| 4. #26018392 | C2 | semidirect |
| 5. C89×#2218 | C2 | semidirect |
| 13. #19151432 | C22 | semidirect |
| 14. C2×D16×C89 | C22 | semidirect |
| 17. #367×C89 | C22 | semidirect |
| 28. Dic712 | D4 | semidirect |
| 32. D1424 | D4 | semidirect |
| 114. #2218 | D89 | semidirect |
| 117. C89 | #13667 | semidirect |
| 123. C2×D16 | C2×D89 | semidirect |
| 129. #367 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033388 | 2 |
| #26022565 | 2 |
| #26018438 | 2 |
| #26018392 | 2 |
| C89×#2218 | 2 |
| #13667 | 89 |