Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
178 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 8. C2×#15667918 | C4 | semidirect |
| 13. M64×C89 | C4 | semidirect |
| 79. C89 | #7470 | semidirect |
| 84. M64 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667918 | 2 |
| #26021848 | 2 |
| C2×M64×C89 | 2 |
| #7470 | 89 |