Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 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. #26033240 | C2 | semidirect |
| 2. #26022520 | C2 | semidirect |
| 4. #26022314 | C2 | semidirect |
| 6. #26022301 | C2 | semidirect |
| 7. #26022160 | C2 | semidirect |
| 8. #26022115 | C2 | semidirect |
| 9. C4×Q32×C89 | C2 | semidirect |
| 152. C4×Q32 | D89 | semidirect |
| 153. C89 | #33969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033240 | 2 |
| #26022520 | 2 |
| #26022513 | 2 |
| #26022314 | 2 |
| #26022310 | 2 |
| #26022301 | 2 |
| #26022160 | 2 |
| #26022115 | 2 |
| C4×Q32×C89 | 2 |
| #33969 | 89 |