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. #23775801 | C2 | semidirect |
| 2. #23765594 | C2 | semidirect |
| 3. #23765582 | C2 | semidirect |
| 4. #23765554 | C2 | semidirect |
| 5. #23765504 | C2 | semidirect |
| 6. C4×D1264 | C2 | semidirect |
| 7. #23765233 | C2 | semidirect |
| 8. #23765187 | C2 | semidirect |
| 9. C79×#2253 | C2 | semidirect |
| 140. #2253 | 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 |
|---|---|
| #23775801 | 2 |
| #23765594 | 2 |
| #23765582 | 2 |
| #23765554 | 2 |
| #23765504 | 2 |
| C4×D1264 | 2 |
| #23765233 | 2 |
| #23765187 | 2 |
| C79×#2253 | 2 |
| #33922 | 79 |