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 |
|---|---|---|
| 2. #26022486 | C2 | direct (N × H) |
| 3. C2×#19151401 | C2 | semidirect |
| 5. C2×C4×#13083549 | C2 | semidirect |
| 6. C2×#499×C89 | C2 | semidirect |
| 14. #19151401 | C22 | semidirect |
| 16. C4×#13083549 | C22 | semidirect |
| 19. #499×C89 | C22 | semidirect |
| 116. C2×C89 | #2242 | semidirect |
| 120. C2×#499 | D89 | semidirect |
| 126. C89 | C2×#2242 | semidirect |
| 134. #499 | C2×D89 | semidirect |
| 236. C2 | #26022486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151982 | 2 |
| #26022486 | 2 |
| C2×#19151401 | 2 |
| C2×#19151398 | 2 |
| C2×C4×#13083549 | 2 |
| C2×#499×C89 | 2 |
| C2×#2242 | 89 |