Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
488 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23774544 | C2 | semidirect |
| 4. #23761963 | C2 | semidirect |
| 6. #23761245 | C2 | semidirect |
| 7. C79×#1960 | C2 | semidirect |
| 185. #1960 | D79 | semidirect |
| 189. C79 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774544 | 2 |
| #23774521 | 2 |
| #23773746 | 2 |
| #23761963 | 2 |
| #23761959 | 2 |
| #23761245 | 2 |
| C79×#1960 | 2 |
| #10226 | 79 |