Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1538 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 287 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. C4×#15667993 | C2 | semidirect |
| 3. #26020665 | C2 | semidirect |
| 4. #26020533 | C2 | semidirect |
| 6. C4×#15667927 | C2 | semidirect |
| 9. C22×C4×Dic89 | C22 | semidirect |
| 10. #19151788 | C4 | direct (N × H) |
| 16. #19151470 | C22 | semidirect |
| 17. #19151459 | C22 | semidirect |
| 20. C4×C22⋊Dic89 | C22 | semidirect |
| 21. #19151365 | C22 | semidirect |
| 32. #15667993 | C2×C4 | semidirect |
| 43. #15667927 | C2×C4 | semidirect |
| 82. C22×Dic89 | C22×C4 | semidirect |
| 89. C22⋊Dic89 | C22×C4 | semidirect |
| 190. C4×C89 | #458 | semidirect |
| 209. C89 | C4×#458 | semidirect |
| 396. C4 | #19151788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151788 | 2 |
| C4×#15667993 | 2 |
| #26020665 | 2 |
| #26020533 | 2 |
| #26020200 | 2 |
| C4×#15667927 | 2 |
| C4×H(5,𝔽2)×C89 | 2 |
| C4×#458 | 89 |