Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26021077 | C2 | semidirect |
| 2. #26018966 | C2 | semidirect |
| 3. #26018872 | C2 | semidirect |
| 4. #26018790 | C2 | semidirect |
| 6. #19151655 | C22 | semidirect |
| 8. C2×#15667923 | C22 | semidirect |
| 9. #19151464 | C22 | semidirect |
| 16. #559×C89 | C4 | semidirect |
| 17. #550×C89 | C4 | semidirect |
| 20. D42×C89 | C4 | semidirect |
| 197. C89 | #8497 | semidirect |
| 199. #559 | Dic89 | semidirect |
| 200. #550 | Dic89 | semidirect |
| 203. D42 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021077 | 2 |
| #26018966 | 2 |
| #26018872 | 2 |
| #26018790 | 2 |
| C89×#3543 | 2 |
| #8497 | 89 |