Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 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. #26028847 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. C2×#19151409 | C2 | semidirect |
| 5. C89×#3407 | C2 | semidirect |
| 7. #19152415 | C4 | semidirect |
| 9. #19152403 | C4 | semidirect |
| 14. #19151636 | C22 | semidirect |
| 15. C2×#15667944 | C22 | semidirect |
| 16. #19151409 | C22 | semidirect |
| 17. #19151409 | C22 | semidirect |
| 20. C2×M32×C89 | C22 | semidirect |
| 31. #15668034 | C2×C4 | semidirect |
| 33. C2×Dic356 | C2×C4 | semidirect |
| 35. C2×D712 | C2×C4 | semidirect |
| 127. #3407 | D89 | semidirect |
| 131. C89 | #33388 | semidirect |
| 141. C2×M32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| #26028847 | 2 |
| #26021989 | 2 |
| C2×#19151409 | 2 |
| C89×#3407 | 2 |
| #33388 | 89 |