Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
882 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 171 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×C89⋊#564 | C2 | semidirect |
| 3. #26019553 | C2 | direct (N × H) |
| 4. C2×#19151340 | C2 | semidirect |
| 5. C2×#19151339 | C2 | semidirect |
| 9. C89⋊#564 | C22 | semidirect |
| 19. #19151340 | C22 | semidirect |
| 20. #19151339 | C22 | semidirect |
| 137. C2×C89 | #1658 | semidirect |
| 146. C89 | C2×#1658 | semidirect |
| 276. C2 | #26019553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C89⋊#564 | 2 |
| C2×#19151962 | 2 |
| #26019553 | 2 |
| C2×#19151340 | 2 |
| C2×#19151339 | 2 |
| C2×#490×C89 | 2 |
| C2×#1658 | 89 |