Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
388 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 81. C22⋊Dic89 | Q16 | semidirect |
| 186. C89 | #12254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027375 | 2 |
| #26021604 | 2 |
| #26019277 | 2 |
| #26018277 | 2 |
| #26018273 | 2 |
| #26018201 | 2 |
| C89×#1602 | 2 |
| #12254 | 89 |