Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 20. #19151396 | C4 | semidirect |
| 201. C89 | #12973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023340 | 2 |
| C2×#19151396 | 2 |
| #26020645 | 2 |
| #26020467 | 2 |
| #26018379 | 2 |
| #26018378 | 2 |
| C89×#1857 | 2 |
| #12973 | 89 |