Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 476 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 |
|---|---|---|
| 3. #23764376 | C2 | semidirect |
| 5. #23761822 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1299 | C2 | semidirect |
| 11. #19098849 | C4 | semidirect |
| 12. #19098844 | C4 | semidirect |
| 13. #19098774 | C4 | semidirect |
| 14. #19098769 | C4 | semidirect |
| 211. #1299 | D79 | semidirect |
| 213. C79 | #8972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773472 | 2 |
| #23772530 | 2 |
| #23764376 | 2 |
| C4×#14579087 | 2 |
| #23761822 | 2 |
| #23761232 | 2 |
| C79×#1299 | 2 |
| #8972 | 79 |