Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
250 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 67 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×#19151437 | C2 | semidirect |
| 2. C2×#19151436 | C2 | semidirect |
| 3. C2×#19151435 | C2 | semidirect |
| 4. #26022503 | C2 | semidirect |
| 6. C32×Dic89 | C2 | semidirect |
| 7. C2×SD64×C89 | C2 | semidirect |
| 37. #15667918 | D4 | semidirect |
| 45. C32×C89 | D4 | semidirect |
| 95. Dic89 | SD64 | semidirect |
| 104. C2×SD64 | D89 | semidirect |
| 108. C89 | #13727 | semidirect |
| 146. C32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151437 | 2 |
| C2×#19151436 | 2 |
| C2×#19151435 | 2 |
| #26022503 | 2 |
| #26022500 | 2 |
| C32×Dic89 | 2 |
| C2×SD64×C89 | 2 |
| #13727 | 89 |