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. #23763480 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761277 | C2 | semidirect |
| 7. C79×#1824 | C2 | semidirect |
| 10. #19098893 | C4 | semidirect |
| 12. #19098876 | C4 | semidirect |
| 217. #1824 | D79 | semidirect |
| 222. C79 | #9521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773323 | 2 |
| #23772445 | 2 |
| #23763480 | 2 |
| #23761941 | 2 |
| #23761306 | 2 |
| #23761277 | 2 |
| C79×#1824 | 2 |
| #9521 | 79 |