Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26022024 | C2 | semidirect |
| 2. #26022017 | C2 | semidirect |
| 6. #26021030 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 146. #1386 | D89 | semidirect |
| 147. C89 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022024 | 2 |
| #26022017 | 2 |
| C2×#19151407 | 2 |
| #26021981 | 2 |
| #26021148 | 2 |
| #26021030 | 2 |
| C89×#1386 | 2 |
| #13469 | 89 |