Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #23762015 | C2 | semidirect |
| 5. #23761300 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#1503 | C2 | semidirect |
| 10. #19098840 | C4 | semidirect |
| 11. #19098840 | C4 | semidirect |
| 12. #19098765 | C4 | semidirect |
| 13. #19098765 | C4 | semidirect |
| 215. #1503 | D79 | semidirect |
| 218. C79 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773495 | 2 |
| #23772434 | 2 |
| #23763228 | 2 |
| #23762015 | 2 |
| #23761300 | 2 |
| #23761256 | 2 |
| C79×#1503 | 2 |
| #9165 | 79 |