Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23774054 | C2 | semidirect |
| 3. #23765620 | C2 | semidirect |
| 4. #23765617 | C2 | semidirect |
| 5. #23765574 | C2 | semidirect |
| 6. #23765479 | C2 | semidirect |
| 8. #23765292 | C2 | semidirect |
| 9. #23765288 | C2 | semidirect |
| 10. #23765213 | C2 | semidirect |
| 15. #19098963 | C22 | semidirect |
| 16. #19098941 | C22 | semidirect |
| 24. #19098670 | C22 | semidirect |
| 25. #19098669 | C22 | semidirect |
| 30. #19098386 | C22 | semidirect |
| 31. #19098385 | C22 | semidirect |
| 32. #19098383 | C22 | semidirect |
| 33. #19098380 | C22 | semidirect |
| 34. #19098379 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 209. C79 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774054 | 2 |
| #23772303 | 2 |
| #23765620 | 2 |
| #23765617 | 2 |
| #23765574 | 2 |
| #23765479 | 2 |
| #23765351 | 2 |
| #23765292 | 2 |
| #23765288 | 2 |
| #23765213 | 2 |
| C79×#2191 | 2 |
| #33693 | 79 |