Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26022570 | C2 | semidirect |
| 3. #26022374 | C2 | semidirect |
| 4. #26018445 | C2 | semidirect |
| 5. #26018437 | C2 | semidirect |
| 6. #26018393 | C2 | semidirect |
| 7. C2×Q64×C89 | C2 | semidirect |
| 119. C2×Q64 | D89 | semidirect |
| 124. C89 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033401 | 2 |
| #26022570 | 2 |
| #26022374 | 2 |
| #26018445 | 2 |
| #26018437 | 2 |
| #26018393 | 2 |
| C2×Q64×C89 | 2 |
| #13672 | 89 |