Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. Q32×Dic89 | C2 | semidirect |
| 4. #26018451 | C2 | semidirect |
| 6. #26018385 | C2 | semidirect |
| 7. C89×#1416 | C2 | semidirect |
| 11. #19151435 | C4 | semidirect |
| 30. #15667918 | C2×C4 | semidirect |
| 33. Q32×C89 | C2×C4 | semidirect |
| 90. #1416 | D89 | semidirect |
| 93. C89 | #13652 | semidirect |
| 111. Q32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151435 | 2 |
| Q32×Dic89 | 2 |
| #26022098 | 2 |
| #26018451 | 2 |
| #26018431 | 2 |
| #26018385 | 2 |
| C89×#1416 | 2 |
| #13652 | 89 |