Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23764233 | C2 | semidirect |
| 3. #23762123 | C2 | semidirect |
| 4. #23761909 | C2 | semidirect |
| 5. C79×#1536 | C2 | semidirect |
| 7. #19099279 | C4 | semidirect |
| 10. #19099198 | C4 | semidirect |
| 14. #19098587 | C22 | semidirect |
| 16. #19098409 | C22 | semidirect |
| 21. #432×C79 | C22 | semidirect |
| 158. #1536 | D79 | semidirect |
| 160. C79 | #8491 | semidirect |
| 170. #432 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23764233 | 2 |
| #23762123 | 2 |
| #23761909 | 2 |
| C79×#1536 | 2 |
| #8491 | 79 |