Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
180 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #26018456 | C2 | semidirect |
| 4. #26018445 | C2 | semidirect |
| 5. C2×Q64×C89 | C2 | semidirect |
| 67. C2×Q64 | D89 | semidirect |
| 72. C89 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022545 | 2 |
| #26022374 | 2 |
| #26018456 | 2 |
| #26018445 | 2 |
| C2×Q64×C89 | 2 |
| #13701 | 89 |