Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23774059 | C2 | semidirect |
| 2. #23765619 | C2 | semidirect |
| 3. #23765576 | C2 | semidirect |
| 4. #23765481 | C2 | semidirect |
| 6. #23765291 | C2 | semidirect |
| 7. #23765216 | C2 | semidirect |
| 11. #19098965 | C22 | semidirect |
| 12. #19098943 | C22 | semidirect |
| 16. #19098671 | C22 | semidirect |
| 18. #19098387 | C22 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 20. #19098378 | C22 | semidirect |
| 23. #19098341 | C22 | semidirect |
| 169. C79 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774059 | 2 |
| #23765619 | 2 |
| #23765576 | 2 |
| #23765481 | 2 |
| #23765351 | 2 |
| #23765291 | 2 |
| #23765216 | 2 |
| C79×#2955 | 2 |
| #33693 | 79 |