Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23764233 | C2 | semidirect |
| 3. #23762131 | C2 | semidirect |
| 4. #23762123 | C2 | semidirect |
| 5. #23761913 | C2 | semidirect |
| 6. #23761909 | C2 | semidirect |
| 7. C79×#1536 | C2 | semidirect |
| 9. #19099274 | C4 | semidirect |
| 12. #19099233 | C4 | semidirect |
| 226. #1536 | D79 | semidirect |
| 229. C79 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777798 | 2 |
| #23764233 | 2 |
| #23762131 | 2 |
| #23762123 | 2 |
| #23761913 | 2 |
| #23761909 | 2 |
| C79×#1536 | 2 |
| #8493 | 79 |