Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23773942 | C2 | semidirect |
| 5. #23761913 | C2 | semidirect |
| 6. #23761292 | C2 | semidirect |
| 7. C79×#1556 | C2 | semidirect |
| 188. #1556 | D79 | semidirect |
| 192. C79 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774405 | 2 |
| #23773942 | 2 |
| #23769512 | 2 |
| #23761999 | 2 |
| #23761913 | 2 |
| #23761292 | 2 |
| C79×#1556 | 2 |
| #10102 | 79 |