Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26019010 | C2 | semidirect |
| 4. #26018937 | C2 | semidirect |
| 6. #26018539 | C2 | semidirect |
| 7. C89×#1997 | C2 | semidirect |
| 146. #1997 | D89 | semidirect |
| 152. C89 | #9812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151946 | 2 |
| #26021092 | 2 |
| #26019010 | 2 |
| #26018937 | 2 |
| #26018921 | 2 |
| #26018539 | 2 |
| C89×#1997 | 2 |
| #9812 | 89 |