Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 516 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. #23772521 | C2 | semidirect |
| 3. #23764229 | C2 | semidirect |
| 4. C4×#14579087 | C2 | semidirect |
| 5. #23761290 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1484 | C2 | semidirect |
| 10. #19098855 | C4 | semidirect |
| 11. #19098850 | C4 | semidirect |
| 12. #19098760 | C4 | semidirect |
| 13. #19098755 | C4 | semidirect |
| 172. D316 | #104 | semidirect |
| 221. #1484 | D79 | semidirect |
| 224. C79 | #8969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773454 | 2 |
| #23772521 | 2 |
| #23764229 | 2 |
| C4×#14579087 | 2 |
| #23761290 | 2 |
| #23761232 | 2 |
| C79×#1484 | 2 |
| #8969 | 79 |