Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 54. #13083549 | Q16 | semidirect |
| 102. C89 | #12459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022532 | 2 |
| #26022154 | 2 |
| #26019653 | 2 |
| #26019647 | 2 |
| #26018325 | 2 |
| #26018306 | 2 |
| C89×#1365 | 2 |
| #12459 | 89 |