Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
270 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 123. C89 | #12409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022532 | 2 |
| #26022404 | 2 |
| #26019656 | 2 |
| #26018307 | 2 |
| Q8⋊#13083549 | 2 |
| #26018216 | 2 |
| C89×#3383 | 2 |
| #12409 | 89 |