Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #23772380 | C2 | semidirect |
| 3. #23761975 | C2 | semidirect |
| 4. #23761817 | C2 | semidirect |
| 5. #23761264 | C2 | semidirect |
| 6. #23761263 | C2 | semidirect |
| 7. C79×#1514 | C2 | semidirect |
| 9. #19098955 | C4 | semidirect |
| 10. #19098950 | C4 | semidirect |
| 11. #19098931 | C4 | semidirect |
| 12. #19098927 | C4 | semidirect |
| 208. #1514 | D79 | semidirect |
| 212. C79 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774437 | 2 |
| #23772380 | 2 |
| #23761975 | 2 |
| #23761817 | 2 |
| #23761264 | 2 |
| #23761263 | 2 |
| C79×#1514 | 2 |
| #9370 | 79 |