Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
844 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 5. C2×#15667919 | C4 | semidirect |
| 8. C2×C22⋊C8×C89 | C4 | semidirect |
| 145. C89 | #7035 | semidirect |
| 149. C2×C22⋊C8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018475 | 2 |
| C89×#1779 | 2 |
| #7035 | 89 |