Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23773349 | C2 | semidirect |
| 4. #23763475 | C2 | semidirect |
| 5. #23761934 | C2 | semidirect |
| 7. C79×#1306 | C2 | semidirect |
| 219. #1306 | D79 | semidirect |
| 220. C79 | #9984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773349 | 2 |
| #23773341 | 2 |
| #23771430 | 2 |
| #23763475 | 2 |
| #23761934 | 2 |
| #23761930 | 2 |
| C79×#1306 | 2 |
| #9984 | 79 |