Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 298 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×#19152027 | C2 | semidirect |
| 2. C2×#19151437 | C2 | semidirect |
| 3. C2×#19151433 | C2 | semidirect |
| 4. #26022339 | C2 | semidirect |
| 5. #26018432 | C2 | semidirect |
| 6. #26018389 | C2 | semidirect |
| 7. C89×#1415 | C2 | semidirect |
| 32. Dic712 | D4 | semidirect |
| 43. D16×C89 | D4 | semidirect |
| 120. #1415 | D89 | semidirect |
| 122. C89 | #13663 | semidirect |
| 153. D16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152027 | 2 |
| C2×#19151437 | 2 |
| C2×#19151433 | 2 |
| #26022339 | 2 |
| #26018432 | 2 |
| #26018389 | 2 |
| C89×#1415 | 2 |
| #13663 | 89 |