Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
982 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 267 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×#19151978 | C2 | semidirect |
| 3. C2×#19151945 | C2 | semidirect |
| 4. #26019858 | C2 | direct (N × H) |
| 5. C2×C82×C89 | C2 | semidirect |
| 11. #19151978 | C22 | semidirect |
| 15. #19151945 | C22 | semidirect |
| 19. C82×C89 | C22 | semidirect |
| 98. C2×C89 | #1709 | semidirect |
| 106. C2×C82 | D89 | semidirect |
| 107. C89 | C2×#1709 | semidirect |
| 121. C82 | C2×D89 | semidirect |
| 200. C2 | #26019858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151978 | 2 |
| C2×#19151975 | 2 |
| C2×#19151945 | 2 |
| #26019858 | 2 |
| C2×C82×C89 | 2 |
| C2×#1709 | 89 |