Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19098965 | C2 | semidirect |
| 3. #23761500 | C2 | semidirect |
| 4. #23761482 | C2 | semidirect |
| 120. C79 | #13372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098965 | 2 |
| C2×#19098373 | 2 |
| #23761500 | 2 |
| #23761482 | 2 |
| C79×#1974 | 2 |
| #13372 | 79 |