Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26021851 | C2 | semidirect |
| 5. #26018341 | C2 | semidirect |
| 6. #26018337 | C2 | semidirect |
| 7. C89×#2153 | C2 | semidirect |
| 142. #2153 | D89 | semidirect |
| 149. C89 | #13123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021881 | 2 |
| C2×#19151383 | 2 |
| #26021851 | 2 |
| #26020053 | 2 |
| #26018341 | 2 |
| #26018337 | 2 |
| C89×#2153 | 2 |
| #13123 | 89 |