Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 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. #23763566 | C2 | semidirect |
| 4. #23761282 | C2 | semidirect |
| 14. #19098303 | C4 | semidirect |
| 31. #14579072 | C2×C4 | semidirect |
| 148. C79 | #8910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766574 | 2 |
| #23763566 | 2 |
| C2×#19098303 | 2 |
| #23761282 | 2 |
| C79×#1959 | 2 |
| #8910 | 79 |