Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1722 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 251 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×#19151970 | C2 | semidirect |
| 2. C2×#19151888 | C2 | semidirect |
| 3. #26019368 | C2 | direct (N × H) |
| 4. C2×#19151342 | C2 | semidirect |
| 5. C2×D4⋊#10623494 | C2 | semidirect |
| 8. C2×#15668012 | C22 | semidirect |
| 10. #19151970 | C22 | semidirect |
| 12. #19151888 | C22 | semidirect |
| 14. C2×C4⋊#10623494 | C22 | semidirect |
| 16. C2×C4×#10623494 | C22 | semidirect |
| 17. #19151342 | C22 | semidirect |
| 18. D4⋊#10623494 | C22 | semidirect |
| 34. #15668012 | C23 | semidirect |
| 38. C4⋊#10623494 | C23 | semidirect |
| 41. C4×#10623494 | C23 | semidirect |
| 96. C2×D4×C89 | SD16 | semidirect |
| 133. D4×C89 | C2×SD16 | semidirect |
| 173. C2×C89 | #1629 | semidirect |
| 182. C89 | C2×#1629 | semidirect |
| 264. C2×D4 | #13083562 | semidirect |
| 311. D4 | C2×#13083562 | semidirect |
| 348. C2 | #26019368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151970 | 2 |
| C2×#19151888 | 2 |
| #26019368 | 2 |
| C2×#19151342 | 2 |
| C2×D4⋊#10623494 | 2 |
| C2×D42×C89 | 2 |
| C2×#1629 | 89 |