Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
314 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23765172 | C2 | semidirect |
| 5. #23761503 | C2 | semidirect |
| 6. #23761484 | C2 | semidirect |
| 7. C79×#1773 | C2 | semidirect |
| 15. #19098378 | C4 | semidirect |
| 16. #19098375 | C4 | semidirect |
| 143. #1773 | D79 | semidirect |
| 146. C79 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765172 | 2 |
| #23765147 | 2 |
| #23765135 | 2 |
| #23764293 | 2 |
| #23761503 | 2 |
| #23761484 | 2 |
| C79×#1773 | 2 |
| #13140 | 79 |