Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
740 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 740 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 |
|---|---|---|
| 2. C2×#19151397 | C2 | semidirect |
| 3. C2×#19151396 | C2 | semidirect |
| 6. #26020645 | C2 | semidirect |
| 7. C89×#1886 | C2 | semidirect |
| 11. #19152347 | C4 | semidirect |
| 242. #1886 | D89 | semidirect |
| 243. C89 | #12775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152347 | 2 |
| C2×#19151397 | 2 |
| C2×#19151396 | 2 |
| C2×#19151394 | 2 |
| #26020655 | 2 |
| #26020645 | 2 |
| C89×#1886 | 2 |
| #12775 | 89 |