Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022564 | C2 | semidirect |
| 2. #26022355 | C2 | semidirect |
| 3. #26018439 | C2 | semidirect |
| 4. #26018392 | C2 | semidirect |
| 5. C89×#3414 | C2 | semidirect |
| 6. C2×D1424 | C22 | semidirect |
| 10. #19151432 | C22 | semidirect |
| 11. #19151426 | C22 | semidirect |
| 35. Q32×C89 | D4 | semidirect |
| 39. D16×C89 | D4 | semidirect |
| 112. #3414 | D89 | semidirect |
| 117. C89 | #13667 | semidirect |
| 143. Q32 | C22⋊D89 | semidirect |
| 148. D16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022564 | 2 |
| #26022355 | 2 |
| #26018439 | 2 |
| #26018392 | 2 |
| C89×#3414 | 2 |
| #13667 | 89 |