Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26030990 | C2 | semidirect |
| 2. #26029163 | C2 | semidirect |
| 3. #26022467 | C2 | semidirect |
| 4. #26022424 | C2 | semidirect |
| 5. #26022329 | C2 | semidirect |
| 6. #26022200 | C2 | semidirect |
| 7. #26022152 | C2 | semidirect |
| 8. C89×#2165 | C2 | semidirect |
| 13. #19151996 | C22 | semidirect |
| 14. #19151975 | C22 | semidirect |
| 23. #19151711 | C22 | semidirect |
| 26. #19151421 | C22 | semidirect |
| 27. #19151412 | C22 | semidirect |
| 30. #364×C89 | C22 | semidirect |
| 32. #347×C89 | C22 | semidirect |
| 87. Dic356 | #41 | semidirect |
| 93. D712 | #41 | semidirect |
| 177. #2165 | D89 | semidirect |
| 178. C89 | #33688 | semidirect |
| 198. #364 | C2×D89 | semidirect |
| 202. #347 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030990 | 2 |
| #26029163 | 2 |
| #26022467 | 2 |
| #26022424 | 2 |
| #26022329 | 2 |
| #26022200 | 2 |
| #26022152 | 2 |
| C89×#2165 | 2 |
| #33688 | 89 |