Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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×#19151432 | C2 | semidirect |
| 3. #26018438 | C2 | semidirect |
| 4. C89×#2158 | C2 | semidirect |
| 8. #19152030 | C4 | semidirect |
| 10. C2×Dic712 | C4 | semidirect |
| 12. C2×D1424 | C4 | semidirect |
| 14. #19151432 | C22 | semidirect |
| 18. #367×C89 | C22 | semidirect |
| 115. #2158 | D89 | semidirect |
| 117. C89 | #13622 | semidirect |
| 131. #367 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| C2×#19151432 | 2 |
| #26018438 | 2 |
| C89×#2158 | 2 |
| #13622 | 89 |