Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1266 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 10. C2×C4×Dic178 | C4 | semidirect |
| 11. C2×#15667977 | C4 | semidirect |
| 142. C89 | #20691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152075 | 2 |
| #26022837 | 2 |
| #26020329 | 2 |
| #26020328 | 2 |
| #26020327 | 2 |
| #26019983 | 2 |
| C89×#1820 | 2 |
| #20691 | 89 |