Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766505 | C2 | semidirect |
| 3. #23762026 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761292 | C2 | semidirect |
| 9. #19098931 | C4 | semidirect |
| 10. #19098927 | C4 | semidirect |
| 197. C79 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773800 | 2 |
| #23766505 | 2 |
| #23762026 | 2 |
| #23761908 | 2 |
| #23761293 | 2 |
| #23761292 | 2 |
| C79×#1505 | 2 |
| #9442 | 79 |