Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
610 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 610 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 |
|---|---|---|
| 1. C2×#19152000 | C2 | semidirect |
| 3. #26022484 | C2 | direct (N × H) |
| 4. C2×#19151403 | C2 | semidirect |
| 6. C2×C4×C16×C89 | C2 | semidirect |
| 13. #19152000 | C22 | semidirect |
| 18. #19151403 | C22 | semidirect |
| 22. C4×C16×C89 | C22 | semidirect |
| 116. C2×C89 | #2242 | semidirect |
| 125. C2×C4×C16 | D89 | semidirect |
| 126. C89 | C2×#2242 | semidirect |
| 142. C4×C16 | C2×D89 | semidirect |
| 236. C2 | #26022484 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152000 | 2 |
| C2×#19151982 | 2 |
| #26022484 | 2 |
| C2×#19151403 | 2 |
| C2×#19151400 | 2 |
| C2×C4×C16×C89 | 2 |
| C2×#2242 | 89 |