Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26022570 | C2 | direct (N × H) |
| 3. C2×#19151438 | C2 | semidirect |
| 4. C2×#19151435 | C2 | semidirect |
| 5. C2×#19151432 | C2 | semidirect |
| 6. C22×Q32×C89 | C2 | semidirect |
| 13. #19151438 | C22 | semidirect |
| 14. #19151435 | C22 | semidirect |
| 15. #19151432 | C22 | semidirect |
| 21. C2×Q32×C89 | C22 | semidirect |
| 108. C2×C89 | #2264 | semidirect |
| 112. C22×Q32 | D89 | semidirect |
| 117. C89 | C2×#2264 | semidirect |
| 126. C2×Q32 | C2×D89 | semidirect |
| 219. C2 | #26022570 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| #26022570 | 2 |
| C2×#19151438 | 2 |
| C2×#19151435 | 2 |
| C2×#19151432 | 2 |
| C22×Q32×C89 | 2 |
| C2×#2264 | 89 |