Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23773432 | C2 | semidirect |
| 3. #23766686 | C2 | semidirect |
| 4. #23764232 | C2 | semidirect |
| 5. #23761830 | C2 | semidirect |
| 6. #23761826 | C2 | semidirect |
| 7. C79×#1274 | C2 | semidirect |
| 223. #1274 | D79 | semidirect |
| 224. C79 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773432 | 2 |
| #23773401 | 2 |
| #23766686 | 2 |
| #23764232 | 2 |
| #23761830 | 2 |
| #23761826 | 2 |
| C79×#1274 | 2 |
| #10013 | 79 |