Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022493 | C2 | semidirect |
| 2. #26022429 | C2 | semidirect |
| 4. #26022093 | C2 | semidirect |
| 5. #26018319 | C2 | semidirect |
| 6. #26018314 | C2 | semidirect |
| 7. C89×#1357 | C2 | semidirect |
| 102. #1357 | D89 | semidirect |
| 103. C89 | #12465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022493 | 2 |
| #26022429 | 2 |
| #26022325 | 2 |
| #26022093 | 2 |
| #26018319 | 2 |
| #26018314 | 2 |
| C89×#1357 | 2 |
| #12465 | 89 |