Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19098601 | C2 | semidirect |
| 2. #23765605 | C2 | semidirect |
| 3. #23765588 | C2 | semidirect |
| 4. #23765189 | C2 | semidirect |
| 5. #23765112 | C2 | semidirect |
| 6. #23765011 | C2 | semidirect |
| 14. #19098390 | C22 | semidirect |
| 15. #19098388 | C22 | semidirect |
| 16. #19098367 | C22 | semidirect |
| 17. #19098364 | C22 | semidirect |
| 151. C79 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098601 | 2 |
| #23765605 | 2 |
| #23765588 | 2 |
| #23765189 | 2 |
| #23765112 | 2 |
| #23765011 | 2 |
| C79×#3050 | 2 |
| #33647 | 79 |