Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
440 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 30. #15667923 | Q8 | semidirect |
| 140. C89 | #9895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028630 | 2 |
| #26020001 | 2 |
| #26018134 | 2 |
| C89×#1767 | 2 |
| #9895 | 89 |