Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23773932 | C2 | semidirect |
| 5. #23761505 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 7. C79×#1384 | C2 | semidirect |
| 30. C2×Dic316 | Q8 | semidirect |
| 32. C2×D632 | Q8 | semidirect |
| 162. #1384 | D79 | semidirect |
| 164. C79 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773932 | 2 |
| #23765135 | 2 |
| C2×#19098374 | 2 |
| #23764296 | 2 |
| #23761505 | 2 |
| #23761487 | 2 |
| C79×#1384 | 2 |
| #13374 | 79 |