Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23774791 | C2 | semidirect |
| 3. #23764378 | C2 | semidirect |
| 4. #23764376 | C2 | semidirect |
| 6. C79⋊#1309 | C2 | semidirect |
| 215. C79 | #10302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774791 | 2 |
| #23774787 | 2 |
| #23764378 | 2 |
| #23764376 | 2 |
| #23764229 | 2 |
| C79⋊#1309 | 2 |
| C79×#3254 | 2 |
| #10302 | 79 |