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. #23762120 | C2 | semidirect |
| 3. #23762035 | C2 | semidirect |
| 4. #23761907 | C2 | semidirect |
| 5. C79×#1963 | C2 | semidirect |
| 7. #19099279 | C4 | semidirect |
| 10. #19099198 | C4 | semidirect |
| 14. #19098620 | C22 | semidirect |
| 20. #423×C79 | C22 | semidirect |
| 22. #376×C79 | C22 | semidirect |
| 156. #1963 | D79 | semidirect |
| 160. C79 | #8491 | semidirect |
| 171. #423 | C2×D79 | semidirect |
| 173. #376 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23762120 | 2 |
| #23762035 | 2 |
| #23761907 | 2 |
| C79×#1963 | 2 |
| #8491 | 79 |