Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
320 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26021938 | C2 | semidirect |
| 3. #26021925 | C2 | semidirect |
| 4. #26018428 | C2 | semidirect |
| 5. #26018426 | C2 | semidirect |
| 6. #26018409 | C2 | semidirect |
| 7. C89×#1406 | C2 | semidirect |
| 8. #19152202 | C4 | semidirect |
| 10. #19151970 | C4 | semidirect |
| 11. #19151967 | C4 | semidirect |
| 17. #19151660 | C4 | semidirect |
| 166. #1406 | D89 | semidirect |
| 167. C89 | #13606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031308 | 2 |
| #26021938 | 2 |
| #26021925 | 2 |
| #26018428 | 2 |
| #26018426 | 2 |
| #26018409 | 2 |
| C89×#1406 | 2 |
| #13606 | 89 |