Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
984 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 175 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. #26021683 | C2 | semidirect |
| 3. #26021455 | C2 | semidirect |
| 4. #26021452 | C2 | semidirect |
| 5. #26021260 | C2 | semidirect |
| 8. C22×#13083564 | C22 | semidirect |
| 10. C2×#15667945 | C22 | semidirect |
| 11. C2×#15667936 | C22 | semidirect |
| 12. C2×#15667935 | C22 | semidirect |
| 18. #19151360 | C22 | semidirect |
| 19. #19151360 | C22 | semidirect |
| 70. C24×C89 | Q16 | semidirect |
| 157. C89 | #32710 | semidirect |
| 206. C24 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028539 | 2 |
| #26021683 | 2 |
| #26021455 | 2 |
| #26021452 | 2 |
| #26021260 | 2 |
| #26020162 | 2 |
| C89×#2848 | 2 |
| #32710 | 89 |