Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022024 | C2 | semidirect |
| 3. C2×#19151420 | C2 | semidirect |
| 6. #26018364 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 9. #19152016 | C4 | semidirect |
| 144. #1386 | D89 | semidirect |
| 145. C89 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26022024 | 2 |
| C2×#19151420 | 2 |
| #26020312 | 2 |
| #26020303 | 2 |
| #26018364 | 2 |
| C89×#1386 | 2 |
| #12833 | 89 |