Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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×#19151431 | C2 | semidirect |
| 3. #26022344 | C2 | semidirect |
| 5. #26018432 | C2 | semidirect |
| 6. #26018429 | C2 | semidirect |
| 7. C89×#1423 | C2 | semidirect |
| 39. C32×C89 | D4 | semidirect |
| 100. #1423 | D89 | semidirect |
| 103. C89 | #13699 | semidirect |
| 135. C32 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151437 | 2 |
| C2×#19151431 | 2 |
| #26022344 | 2 |
| #26022339 | 2 |
| #26018432 | 2 |
| #26018429 | 2 |
| C89×#1423 | 2 |
| #13699 | 89 |