Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 126. C89 | #9788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152000 | 2 |
| #26019015 | 2 |
| #26018853 | 2 |
| #26018607 | 2 |
| C8×M16×C89 | 2 |
| #9788 | 89 |