Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23766295 | C2 | semidirect |
| 3. #23763500 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761286 | C2 | semidirect |
| 12. #19098603 | C4 | semidirect |
| 13. #19098568 | C4 | semidirect |
| 210. C79 | #9366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773336 | 2 |
| #23766295 | 2 |
| #23763500 | 2 |
| #23761916 | 2 |
| #23761306 | 2 |
| #23761286 | 2 |
| C79×#1964 | 2 |
| #9366 | 79 |