Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 203 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. #26022495 | C2 | direct (N × H) |
| 3. C2×#19151398 | C2 | semidirect |
| 4. C2×#19151374 | C2 | semidirect |
| 5. C2×#499×C89 | C2 | semidirect |
| 12. #19151398 | C22 | semidirect |
| 13. #19151374 | C22 | semidirect |
| 16. #499×C89 | C22 | semidirect |
| 98. C2×C89 | #2244 | semidirect |
| 102. C2×#499 | D89 | semidirect |
| 107. C89 | C2×#2244 | semidirect |
| 114. #499 | C2×D89 | semidirect |
| 200. C2 | #26022495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151975 | 2 |
| #26022495 | 2 |
| C2×#19151398 | 2 |
| C2×#19151374 | 2 |
| C2×#499×C89 | 2 |
| C2×#2244 | 89 |