Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 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. #23774600 | C2 | semidirect |
| 2. #23773500 | C2 | semidirect |
| 4. #23762034 | C2 | semidirect |
| 5. #23761874 | C2 | semidirect |
| 6. #23761740 | C2 | semidirect |
| 7. C79×#1287 | C2 | semidirect |
| 202. #1287 | D79 | semidirect |
| 203. C79 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774600 | 2 |
| #23773500 | 2 |
| #23773401 | 2 |
| #23762034 | 2 |
| #23761874 | 2 |
| #23761740 | 2 |
| C79×#1287 | 2 |
| #10042 | 79 |