Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 7. #19151367 | C4 | semidirect |
| 9. #19151324 | C4 | semidirect |
| 171. C89 | #7215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020332 | 2 |
| #26018582 | 2 |
| C89×#1436 | 2 |
| #7215 | 89 |