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. #23764231 | C2 | semidirect |
| 3. #23762120 | C2 | semidirect |
| 4. #23762034 | C2 | semidirect |
| 5. #23761912 | C2 | semidirect |
| 6. #23761909 | C2 | semidirect |
| 7. C79×#1559 | C2 | semidirect |
| 10. #19099273 | C4 | semidirect |
| 12. #19099235 | C4 | semidirect |
| 224. #1559 | 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 |
|---|---|
| #23777800 | 2 |
| #23764231 | 2 |
| #23762120 | 2 |
| #23762034 | 2 |
| #23761912 | 2 |
| #23761909 | 2 |
| C79×#1559 | 2 |
| #8493 | 79 |