Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26022017 | C2 | semidirect |
| 5. #26021043 | C2 | semidirect |
| 6. #26018355 | C2 | semidirect |
| 7. C89×#2161 | C2 | semidirect |
| 131. #2161 | D89 | semidirect |
| 138. C89 | #13472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022017 | 2 |
| C2×#19151412 | 2 |
| C2×#19151410 | 2 |
| #26021160 | 2 |
| #26021043 | 2 |
| #26018355 | 2 |
| C89×#2161 | 2 |
| #13472 | 89 |