Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26020288 | C2 | semidirect |
| 4. #26018128 | C2 | semidirect |
| 161. C89 | #8613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151670 | 2 |
| #26020288 | 2 |
| #26018590 | 2 |
| #26018128 | 2 |
| C89×#1465 | 2 |
| #8613 | 89 |