Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 286 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. C22×Dic356 | C4 | semidirect |
| 8. #19151361 | C4 | semidirect |
| 120. C89 | #7078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021262 | 2 |
| #26018120 | 2 |
| C89×#1314 | 2 |
| #7078 | 89 |