Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
232 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 59 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×#19151433 | C2 | semidirect |
| 2. #26022500 | C2 | semidirect |
| 3. D16×Dic89 | C2 | semidirect |
| 4. #26018447 | C2 | semidirect |
| 5. #26018431 | C2 | semidirect |
| 6. #26018430 | C2 | semidirect |
| 7. C2×D32×C89 | C2 | semidirect |
| 38. D16×C89 | D4 | semidirect |
| 95. Dic89 | D32 | semidirect |
| 104. C2×D32 | D89 | semidirect |
| 110. C89 | #13685 | semidirect |
| 136. D16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151433 | 2 |
| #26022500 | 2 |
| D16×Dic89 | 2 |
| #26018447 | 2 |
| #26018431 | 2 |
| #26018430 | 2 |
| C2×D32×C89 | 2 |
| #13685 | 89 |