Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19098362 | C2 | semidirect |
| 2. #23762126 | C2 | semidirect |
| 3. #23761554 | C2 | semidirect |
| 8. #19098362 | C22 | semidirect |
| 10. #19098312 | C22 | semidirect |
| 172. C79 | #13573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098362 | 2 |
| #23762126 | 2 |
| #23761554 | 2 |
| C2×#456×C79 | 2 |
| #13573 | 79 |