Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23775804 | C2 | semidirect |
| 2. #23765679 | C2 | semidirect |
| 3. #23765589 | C2 | semidirect |
| 4. #23765579 | C2 | semidirect |
| 5. #23765557 | C2 | semidirect |
| 6. #23765500 | C2 | semidirect |
| 7. #23765233 | C2 | semidirect |
| 8. #23765185 | C2 | semidirect |
| 9. C4×D16×C79 | C2 | semidirect |
| 145. C4×D16 | D79 | semidirect |
| 148. C79 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775804 | 2 |
| #23765679 | 2 |
| #23765589 | 2 |
| #23765579 | 2 |
| #23765557 | 2 |
| #23765500 | 2 |
| #23765233 | 2 |
| #23765185 | 2 |
| C4×D16×C79 | 2 |
| #33922 | 79 |