Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 4. #26018428 | C2 | semidirect |
| 5. #26018426 | C2 | semidirect |
| 6. #26018412 | C2 | semidirect |
| 7. C89×#1407 | C2 | semidirect |
| 8. #19152209 | C4 | semidirect |
| 10. #19151977 | C4 | semidirect |
| 11. #19151967 | C4 | semidirect |
| 17. #19151660 | C4 | semidirect |
| 160. #1407 | D89 | semidirect |
| 161. C89 | #13608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031330 | 2 |
| #26021938 | 2 |
| #26021925 | 2 |
| #26018428 | 2 |
| #26018426 | 2 |
| #26018412 | 2 |
| C89×#1407 | 2 |
| #13608 | 89 |