Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#15667957 | C2 | semidirect |
| 2. C2×#19151874 | C2 | semidirect |
| 4. C2×#19151413 | C2 | semidirect |
| 5. C2×#19151410 | C2 | semidirect |
| 6. #26021865 | C2 | semidirect |
| 7. C89×#1381 | C2 | semidirect |
| 199. #1381 | D89 | semidirect |
| 200. C89 | #13314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667957 | 2 |
| C2×#19151874 | 2 |
| C2×#19151869 | 2 |
| C2×#19151413 | 2 |
| C2×#19151410 | 2 |
| #26021865 | 2 |
| C89×#1381 | 2 |
| #13314 | 89 |