Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
170 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 170 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. #26022047 | C2 | semidirect |
| 3. #26018458 | C2 | semidirect |
| 4. #26018443 | C2 | semidirect |
| 5. C89×#1400 | C2 | semidirect |
| 77. #1400 | D89 | semidirect |
| 78. C89 | #13717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022355 | 2 |
| #26022047 | 2 |
| #26018458 | 2 |
| #26018443 | 2 |
| C89×#1400 | 2 |
| #13717 | 89 |