Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
726 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23765985 | C2 | semidirect |
| 3. #23763323 | C2 | semidirect |
| 5. #23761254 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 9. C2×#14579148 | C4 | semidirect |
| 14. #19098468 | C4 | semidirect |
| 220. C79 | #9466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23767059 | 2 |
| #23765985 | 2 |
| #23763323 | 2 |
| #23761929 | 2 |
| #23761254 | 2 |
| #23761252 | 2 |
| C79×#1510 | 2 |
| #9466 | 79 |