Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
604 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 29. C22⋊#10623494 | Q8 | semidirect |
| 32. #15667919 | Q8 | semidirect |
| 197. C89 | #10570 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020444 | 2 |
| #26018516 | 2 |
| #26018130 | 2 |
| #26018095 | 2 |
| C89×#2659 | 2 |
| #10570 | 89 |