Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. C4×#14579080 | C2 | semidirect |
| 3. #23761527 | C2 | semidirect |
| 7. #19098360 | C4 | semidirect |
| 20. #14579080 | C2×C4 | semidirect |
| 142. C79 | #12632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098360 | 2 |
| C4×#14579080 | 2 |
| #23761527 | 2 |
| C79×#2326 | 2 |
| #12632 | 79 |