Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23766317 | C2 | semidirect |
| 5. #23761794 | C2 | semidirect |
| 6. #23761301 | C2 | semidirect |
| 7. C79×#1286 | C2 | semidirect |
| 13. #19098774 | C4 | semidirect |
| 14. #19098764 | C4 | semidirect |
| 208. #1286 | D79 | semidirect |
| 209. C79 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772874 | 2 |
| #23766317 | 2 |
| #23761959 | 2 |
| #23761896 | 2 |
| #23761794 | 2 |
| #23761301 | 2 |
| C79×#1286 | 2 |
| #9180 | 79 |