Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
426 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 9. #19098959 | C4 | semidirect |
| 10. #19098913 | C4 | semidirect |
| 170. C79 | #9292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774541 | 2 |
| #23772341 | 2 |
| #23764219 | 2 |
| #23762071 | 2 |
| #23761258 | 2 |
| #23761230 | 2 |
| C79×#1518 | 2 |
| #9292 | 79 |