Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 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. C2×#19152031 | C2 | semidirect |
| 2. C2×#19152027 | C2 | semidirect |
| 3. #26022560 | C2 | direct (N × H) |
| 4. C2×#19151438 | C2 | semidirect |
| 5. C2×#19151437 | C2 | semidirect |
| 6. C2×#19151433 | C2 | semidirect |
| 7. C2×C32×D89 | C2 | semidirect |
| 8. C2×SD64×C89 | C2 | semidirect |
| 12. #19152031 | C22 | semidirect |
| 14. #19152027 | C22 | semidirect |
| 20. #19151438 | C22 | semidirect |
| 21. #19151437 | C22 | semidirect |
| 22. #19151433 | C22 | semidirect |
| 24. C32×D89 | C22 | semidirect |
| 27. SD64×C89 | C22 | semidirect |
| 126. C2×C89 | #2262 | semidirect |
| 135. C2×SD64 | D89 | semidirect |
| 138. C89 | C2×#2262 | semidirect |
| 154. SD64 | C2×D89 | semidirect |
| 257. C2 | #26022560 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152031 | 2 |
| C2×#19152027 | 2 |
| #26022560 | 2 |
| C2×#19151438 | 2 |
| C2×#19151437 | 2 |
| C2×#19151433 | 2 |
| C2×C32×D89 | 2 |
| C2×SD64×C89 | 2 |
| C2×#2262 | 89 |