Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 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 |
| 3. #26029908 | C2 | semidirect |
| 4. C2×#19151413 | C2 | semidirect |
| 5. #26021967 | C2 | semidirect |
| 6. C2×#19151381 | C2 | semidirect |
| 7. C89×#1382 | C2 | semidirect |
| 200. #1382 | D89 | semidirect |
| 201. C89 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667957 | 2 |
| C2×#19151869 | 2 |
| #26029908 | 2 |
| C2×#19151413 | 2 |
| #26021967 | 2 |
| C2×#19151381 | 2 |
| C89×#1382 | 2 |
| #13320 | 89 |