Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#19152039 | C2 | semidirect |
| 3. #26021988 | C2 | semidirect |
| 4. #26021972 | C2 | semidirect |
| 5. #26021150 | C2 | semidirect |
| 6. #26018338 | C2 | semidirect |
| 7. C89×#3156 | C2 | semidirect |
| 214. #3156 | D89 | semidirect |
| 219. C89 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| C2×#19152039 | 2 |
| #26021988 | 2 |
| #26021972 | 2 |
| #26021150 | 2 |
| #26018338 | 2 |
| C89×#3156 | 2 |
| #13335 | 89 |