Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
894 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C2×#19151387 | C2 | semidirect |
| 4. #26018369 | C2 | semidirect |
| 6. C2×#15667993 | C4 | semidirect |
| 8. C22×C22⋊Dic89 | C4 | semidirect |
| 14. #19151478 | C4 | semidirect |
| 18. #19151454 | C4 | semidirect |
| 25. C23×Dic89 | C2×C4 | semidirect |
| 26. C23×Dic89 | C2×C4 | semidirect |
| 43. C2×C22⋊Dic89 | C2×C4 | semidirect |
| 44. C2×C22⋊Dic89 | C2×C4 | semidirect |
| 264. C22×C89 | #352 | semidirect |
| 293. C89 | #13084 | semidirect |
| 552. C22 | #19151387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023575 | 2 |
| C2×#19151387 | 2 |
| #26020173 | 2 |
| #26018369 | 2 |
| C22×#99×C89 | 2 |
| #13084 | 89 |