Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 4. C2×#15667946 | C4 | semidirect |
| 8. #19151361 | C4 | semidirect |
| 106. C89 | #7079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021675 | 2 |
| #26018176 | 2 |
| C89×#1289 | 2 |
| #7079 | 89 |