Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
446 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 11. #19098859 | C4 | semidirect |
| 12. #19098849 | C4 | semidirect |
| 186. C79 | #9178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773207 | 2 |
| #23766367 | 2 |
| #23761963 | 2 |
| #23761900 | 2 |
| #23761794 | 2 |
| #23761301 | 2 |
| C79×#1286 | 2 |
| #9178 | 79 |