Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. #23765679 | C2 | semidirect |
| 3. #23765607 | C2 | semidirect |
| 4. #23765601 | C2 | semidirect |
| 5. #23765564 | C2 | semidirect |
| 6. #23765505 | C2 | semidirect |
| 8. #23765185 | C2 | semidirect |
| 9. C4×Q32×C79 | C2 | semidirect |
| 139. C4×Q32 | D79 | semidirect |
| 142. C79 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775770 | 2 |
| #23765679 | 2 |
| #23765607 | 2 |
| #23765601 | 2 |
| #23765564 | 2 |
| #23765505 | 2 |
| #23765233 | 2 |
| #23765185 | 2 |
| C4×Q32×C79 | 2 |
| #33919 | 79 |