Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23772485 | C2 | semidirect |
| 5. #23761297 | C2 | semidirect |
| 6. #23761258 | C2 | semidirect |
| 7. C79×#1805 | C2 | semidirect |
| 11. #19098773 | C4 | semidirect |
| 12. #19098763 | C4 | semidirect |
| 186. #1805 | D79 | semidirect |
| 191. C79 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772872 | 2 |
| #23772485 | 2 |
| #23761959 | 2 |
| #23761798 | 2 |
| #23761297 | 2 |
| #23761258 | 2 |
| C79×#1805 | 2 |
| #9310 | 79 |