Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. C2×#15667931 | C4 | semidirect |
| 9. C2×C22⋊#10623494 | C4 | semidirect |
| 142. C89 | #7309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020180 | 2 |
| #26020164 | 2 |
| C89×#1782 | 2 |
| #7309 | 89 |