Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3798 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 555 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 |
|---|---|---|
| 1. C2×#19151572 | C2 | semidirect |
| 2. #26022743 | C2 | semidirect |
| 3. #26020200 | C2 | semidirect |
| 5. C2×#15667971 | C22 | semidirect |
| 6. C22×C4×Dic89 | C22 | semidirect |
| 8. C2×#15667927 | C22 | semidirect |
| 11. #19151478 | C22 | semidirect |
| 14. #585×C89 | C4 | semidirect |
| 79. C2×Q8×C89 | C22⋊C4 | semidirect |
| 88. C2×D4×C89 | C22⋊C4 | semidirect |
| 96. C22×C4×C89 | C22⋊C4 | semidirect |
| 161. C89 | #20608 | semidirect |
| 163. #585 | Dic89 | semidirect |
| 227. C2×Q8 | C22⋊Dic89 | semidirect |
| 236. C2×D4 | C22⋊Dic89 | semidirect |
| 247. C22×C4 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151572 | 2 |
| #26022743 | 2 |
| #26020200 | 2 |
| C2×#585×C89 | 2 |
| #20608 | 89 |