Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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. #349×D79 | C2 | semidirect |
| 3. #23761338 | C2 | semidirect |
| 4. #23761337 | C2 | semidirect |
| 5. C79×#1321 | C2 | semidirect |
| 15. #19098345 | C22 | semidirect |
| 18. #349×C79 | C22 | semidirect |
| 181. #1321 | D79 | semidirect |
| 182. C79 | #11438 | semidirect |
| 195. #349 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771842 | 2 |
| #349×D79 | 2 |
| #23761338 | 2 |
| #23761337 | 2 |
| C79×#1321 | 2 |
| #11438 | 79 |