Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
676 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772448 | C2 | semidirect |
| 3. #23763345 | C2 | semidirect |
| 4. #23763311 | C2 | semidirect |
| 5. #23761288 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 7. C79×#1501 | C2 | semidirect |
| 11. #19098718 | C4 | semidirect |
| 12. #19098713 | C4 | semidirect |
| 14. #19098701 | C4 | semidirect |
| 15. #19098696 | C4 | semidirect |
| 294. #1501 | D79 | semidirect |
| 297. C79 | #9037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772616 | 2 |
| #23772448 | 2 |
| #23763345 | 2 |
| #23763311 | 2 |
| #23761288 | 2 |
| #23761248 | 2 |
| C79×#1501 | 2 |
| #9037 | 79 |