Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 77 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×#19151388 | C2 | semidirect |
| 3. #26020666 | C2 | semidirect |
| 5. #26020532 | C2 | semidirect |
| 6. #26018370 | C2 | semidirect |
| 267. C89 | #13423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| C2×#19151388 | 2 |
| #26020666 | 2 |
| #26020651 | 2 |
| #26020532 | 2 |
| #26018370 | 2 |
| C89×#2709 | 2 |
| #13423 | 89 |