Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19098891 | C4 | semidirect |
| 13. #19098718 | C4 | semidirect |
| 217. C79 | #9342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774221 | 2 |
| #23764384 | 2 |
| #23761932 | 2 |
| #23761920 | 2 |
| #23761306 | 2 |
| #23761252 | 2 |
| C79×#2378 | 2 |
| #9342 | 79 |