Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 10. #19098855 | C4 | semidirect |
| 11. #19098845 | C4 | semidirect |
| 172. C79 | #9308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773201 | 2 |
| #23772483 | 2 |
| #23763412 | 2 |
| #23761803 | 2 |
| #23761296 | 2 |
| #23761258 | 2 |
| C79×#1518 | 2 |
| #9308 | 79 |