Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. #23772495 | C2 | semidirect |
| 5. #23761311 | C2 | semidirect |
| 6. #23761261 | C2 | semidirect |
| 7. C79×#1559 | C2 | semidirect |
| 171. #1559 | D79 | semidirect |
| 176. C79 | #9530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773495 | 2 |
| #23772495 | 2 |
| #23761824 | 2 |
| #23761740 | 2 |
| #23761311 | 2 |
| #23761261 | 2 |
| C79×#1559 | 2 |
| #9530 | 79 |