Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 472 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. #23763486 | C2 | semidirect |
| 5. #23761305 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 7. C79×#1821 | C2 | semidirect |
| 9. #19098898 | C4 | semidirect |
| 11. #19098881 | C4 | semidirect |
| 220. #1821 | D79 | semidirect |
| 224. C79 | #9522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773323 | 2 |
| #23772450 | 2 |
| #23763486 | 2 |
| #23761944 | 2 |
| #23761305 | 2 |
| #23761276 | 2 |
| C79×#1821 | 2 |
| #9522 | 79 |