Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23774145 | C2 | semidirect |
| 3. #23765620 | C2 | semidirect |
| 4. #23765572 | C2 | semidirect |
| 5. #23765482 | C2 | semidirect |
| 7. #23765293 | C2 | semidirect |
| 8. C79×#2165 | C2 | semidirect |
| 13. #19098961 | C22 | semidirect |
| 14. #19098943 | C22 | semidirect |
| 23. #19098671 | C22 | semidirect |
| 26. #19098386 | C22 | semidirect |
| 27. #19098380 | C22 | semidirect |
| 30. #364×C79 | C22 | semidirect |
| 32. #347×C79 | C22 | semidirect |
| 169. #2165 | D79 | semidirect |
| 170. C79 | #33689 | semidirect |
| 190. #364 | C2×D79 | semidirect |
| 194. #347 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774145 | 2 |
| #23772311 | 2 |
| #23765620 | 2 |
| #23765572 | 2 |
| #23765482 | 2 |
| #23765353 | 2 |
| #23765293 | 2 |
| C79×#2165 | 2 |
| #33689 | 79 |