Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
640 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26028733 | C2 | semidirect |
| 3. #26021944 | C2 | semidirect |
| 4. #26020225 | C2 | semidirect |
| 5. #26018380 | C2 | semidirect |
| 6. #26018374 | C2 | semidirect |
| 7. C89×#2122 | C2 | semidirect |
| 9. C2×#15668038 | C4 | semidirect |
| 10. C22×#13083562 | C4 | semidirect |
| 18. #19151606 | C4 | semidirect |
| 19. #19151592 | C4 | semidirect |
| 249. #2122 | D89 | semidirect |
| 253. C89 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029536 | 2 |
| #26028733 | 2 |
| #26021944 | 2 |
| #26020225 | 2 |
| #26018380 | 2 |
| #26018374 | 2 |
| C89×#2122 | 2 |
| #13098 | 89 |