Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
404 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 27. C22×Dic178 | Q8 | semidirect |
| 34. C2×C4⋊Dic89 | Q8 | semidirect |
| 198. C89 | #10383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021236 | 2 |
| #26018784 | 2 |
| #26018771 | 2 |
| #26018158 | 2 |
| #26018138 | 2 |
| #26018104 | 2 |
| C89×#2665 | 2 |
| #10383 | 89 |