Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3936 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3936 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 1. C2×#19151760 | C2 | semidirect |
| 2. C2×#19151749 | C2 | semidirect |
| 3. #26025981 | C2 | semidirect |
| 4. #26020192 | C2 | semidirect |
| 5. #26020183 | C2 | semidirect |
| 6. #26020164 | C2 | semidirect |
| 8. C22×#13083564 | C22 | semidirect |
| 9. C22×#13083562 | C22 | semidirect |
| 10. C2×#15667991 | C22 | semidirect |
| 13. C2×#15667936 | C22 | semidirect |
| 14. C2×#15667933 | C22 | semidirect |
| 15. C2×#15667933 | C22 | semidirect |
| 16. C2×C22⋊#10623494 | C22 | semidirect |
| 17. C2×C22⋊#10623494 | C22 | semidirect |
| 20. #19151458 | C22 | semidirect |
| 198. C89 | #32886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151760 | 2 |
| C2×#19151749 | 2 |
| #26025981 | 2 |
| #26020192 | 2 |
| #26020183 | 2 |
| #26020164 | 2 |
| C22×H(5,𝔽2)×C89 | 2 |
| #32886 | 89 |