Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #26018358 | C2 | semidirect |
| 8. #19151636 | C4 | semidirect |
| 10. C2×#15667946 | C4 | semidirect |
| 11. C2×#15667946 | C4 | semidirect |
| 142. C89 | #12870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151636 | 2 |
| #26020277 | 2 |
| #26018358 | 2 |
| C89×#2112 | 2 |
| #12870 | 89 |