Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 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. C2×#19152015 | C2 | semidirect |
| 3. #26021979 | C2 | semidirect |
| 4. C2×#19151404 | C2 | semidirect |
| 5. C89×#2916 | C2 | semidirect |
| 13. C2×#15667952 | C22 | semidirect |
| 14. C22×#13083549 | C22 | semidirect |
| 15. #19151404 | C22 | semidirect |
| 16. #19151404 | C22 | semidirect |
| 20. C2×#108×C89 | C22 | semidirect |
| 119. #2916 | D89 | semidirect |
| 122. C89 | #33385 | semidirect |
| 135. C2×#108 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| C2×#19152015 | 2 |
| #26021979 | 2 |
| C2×#19151404 | 2 |
| C89×#2916 | 2 |
| #33385 | 89 |