Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 23. #15667952 | Q8 | semidirect |
| 27. #15667944 | Q8 | semidirect |
| 127. C89 | #13454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022041 | 2 |
| #26020995 | 2 |
| #26018357 | 2 |
| #26018336 | 2 |
| C89×#3162 | 2 |
| #13454 | 89 |