Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. #19151538 | C4 | semidirect |
| 14. #19151519 | C4 | semidirect |
| 215. C89 | #9200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026068 | 2 |
| #26022869 | 2 |
| #26018825 | 2 |
| #26018823 | 2 |
| C2×#19151323 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9200 | 89 |