Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 3. #23763583 | C2 | semidirect |
| 5. #23761285 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 7. C79×#1855 | C2 | semidirect |
| 22. #19098301 | C4 | semidirect |
| 23. #19098301 | C4 | semidirect |
| 24. #19098298 | C4 | semidirect |
| 25. #19098298 | C4 | semidirect |
| 220. #1855 | D79 | semidirect |
| 225. C79 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772450 | 2 |
| #23763702 | 2 |
| #23763583 | 2 |
| #23761892 | 2 |
| #23761285 | 2 |
| #23761246 | 2 |
| C79×#1855 | 2 |
| #8875 | 79 |