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. #23765610 | C2 | semidirect |
| 3. #23765604 | C2 | semidirect |
| 4. #23765561 | C2 | semidirect |
| 5. #23765509 | C2 | semidirect |
| 6. C4×Dic632 | C2 | semidirect |
| 8. #23765187 | C2 | semidirect |
| 9. C79×#2253 | C2 | semidirect |
| 134. #2253 | 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 |
|---|---|
| #23775767 | 2 |
| #23765610 | 2 |
| #23765604 | 2 |
| #23765561 | 2 |
| #23765509 | 2 |
| C4×Dic632 | 2 |
| #23765233 | 2 |
| #23765187 | 2 |
| C79×#2253 | 2 |
| #33919 | 79 |