Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23773349 | C2 | semidirect |
| 4. #23763469 | C2 | semidirect |
| 5. #23761765 | C2 | semidirect |
| 7. C79×#1293 | C2 | semidirect |
| 210. #1293 | D79 | semidirect |
| 211. C79 | #9978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774158 | 2 |
| #23773349 | 2 |
| #23773341 | 2 |
| #23763469 | 2 |
| #23761765 | 2 |
| #23761761 | 2 |
| C79×#1293 | 2 |
| #9978 | 79 |