Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19151428 | C2 | semidirect |
| 2. C2×#19151405 | C2 | semidirect |
| 3. C2×#19151373 | C2 | semidirect |
| 4. #26021141 | C2 | semidirect |
| 17. C2×Q32×C89 | C4 | semidirect |
| 18. C2×SD32×C89 | C4 | semidirect |
| 19. C2×D16×C89 | C4 | semidirect |
| 130. C89 | #13242 | semidirect |
| 134. C2×Q32 | Dic89 | semidirect |
| 135. C2×SD32 | Dic89 | semidirect |
| 136. C2×D16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151428 | 2 |
| C2×#19151405 | 2 |
| C2×#19151373 | 2 |
| #26021141 | 2 |
| C2×#508×C89 | 2 |
| #13242 | 89 |