Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 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. C4×#14579095 | C2 | semidirect |
| 3. #23761413 | C2 | semidirect |
| 5. C79×#2163 | C2 | semidirect |
| 7. #19098965 | C4 | semidirect |
| 8. #19098947 | C4 | semidirect |
| 13. C4×Dic316 | C4 | semidirect |
| 15. C4×D632 | C4 | semidirect |
| 149. #2163 | D79 | semidirect |
| 153. C79 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773970 | 2 |
| C4×#14579095 | 2 |
| #23761413 | 2 |
| #23761410 | 2 |
| C79×#2163 | 2 |
| #11746 | 79 |