Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
350 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23774849 | C2 | semidirect |
| 4. #23761419 | C2 | semidirect |
| 5. #23761418 | C2 | semidirect |
| 6. #23761341 | C2 | semidirect |
| 168. C79 | #12165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774849 | 2 |
| #23765329 | 2 |
| #23764653 | 2 |
| #23761419 | 2 |
| #23761418 | 2 |
| #23761341 | 2 |
| C79×#2187 | 2 |
| #12165 | 79 |