Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766153 | C2 | semidirect |
| 4. #23761932 | C2 | semidirect |
| 5. #23761308 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 11. #19098719 | C4 | semidirect |
| 12. #19098714 | C4 | semidirect |
| 274. C79 | #9524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772660 | 2 |
| #23766153 | 2 |
| #23763344 | 2 |
| #23761932 | 2 |
| #23761308 | 2 |
| #23761252 | 2 |
| C79×#1782 | 2 |
| #9524 | 79 |