Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1838 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1838 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×#19151974 | C2 | semidirect |
| 2. C2×#19151793 | C2 | semidirect |
| 3. #26019306 | C2 | direct (N × H) |
| 4. C2×#19151342 | C2 | semidirect |
| 5. C2×D4⋊#10623494 | C2 | semidirect |
| 6. C2×D42×C89 | C2 | semidirect |
| 9. C2×#15668009 | C22 | semidirect |
| 11. #19151974 | C22 | semidirect |
| 13. #19151793 | C22 | semidirect |
| 14. C2×C4⋊#10623494 | C22 | semidirect |
| 16. C2×C4×#10623494 | C22 | semidirect |
| 17. #19151342 | C22 | semidirect |
| 18. D4⋊#10623494 | C22 | semidirect |
| 22. D42×C89 | C22 | semidirect |
| 37. #15668009 | C23 | semidirect |
| 39. C4⋊#10623494 | C23 | semidirect |
| 42. C4×#10623494 | C23 | semidirect |
| 100. C2×D4×C89 | D8 | semidirect |
| 140. D4×C89 | C2×D8 | semidirect |
| 183. C2×C89 | #1619 | semidirect |
| 187. C2×D42 | D89 | semidirect |
| 193. C89 | C2×#1619 | semidirect |
| 199. D42 | C2×D89 | semidirect |
| 281. C2×D4 | #13083559 | semidirect |
| 332. D4 | C2×#13083559 | semidirect |
| 370. C2 | #26019306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151974 | 2 |
| C2×#19151793 | 2 |
| #26019306 | 2 |
| C2×#19151342 | 2 |
| C2×D4⋊#10623494 | 2 |
| C2×D42×C89 | 2 |
| C2×#1619 | 89 |