Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
618 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 618 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 |
|---|---|---|
| 1. #23772429 | C2 | semidirect |
| 3. #23761967 | C2 | semidirect |
| 4. #23761278 | C2 | semidirect |
| 5. C79×#1799 | C2 | semidirect |
| 12. #19098493 | C4 | semidirect |
| 13. #19098488 | C4 | semidirect |
| 14. #19098480 | C4 | semidirect |
| 15. #19098472 | C4 | semidirect |
| 44. C22⋊(C79⋊C8) | D4 | semidirect |
| 218. #1799 | D79 | semidirect |
| 221. C79 | #9386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772429 | 2 |
| #23768356 | 2 |
| #23761967 | 2 |
| #23761278 | 2 |
| C79×#1799 | 2 |
| #9386 | 79 |