Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
590 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23774530 | C2 | semidirect |
| 3. #23768573 | C2 | semidirect |
| 4. #23762084 | C2 | semidirect |
| 5. #23761896 | C2 | semidirect |
| 6. #23761302 | C2 | semidirect |
| 7. C79×#1478 | C2 | semidirect |
| 219. #1478 | D79 | semidirect |
| 221. C79 | #10241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774530 | 2 |
| #23772864 | 2 |
| #23768573 | 2 |
| #23762084 | 2 |
| #23761896 | 2 |
| #23761302 | 2 |
| C79×#1478 | 2 |
| #10241 | 79 |