Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26020423 | C2 | semidirect |
| 3. #26018704 | C2 | semidirect |
| 4. #26018703 | C2 | semidirect |
| 5. #26018702 | C2 | semidirect |
| 6. C2×#19151320 | C2 | semidirect |
| 7. C89×#1492 | C2 | semidirect |
| 180. #1492 | D89 | semidirect |
| 182. C89 | #9862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030678 | 2 |
| #26020423 | 2 |
| #26018704 | 2 |
| #26018703 | 2 |
| #26018702 | 2 |
| C2×#19151320 | 2 |
| C89×#1492 | 2 |
| #9862 | 89 |