Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 12. #19098859 | C4 | semidirect |
| 13. #19098849 | C4 | semidirect |
| 190. C79 | #9176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773207 | 2 |
| #23766320 | 2 |
| #23761965 | 2 |
| #23761898 | 2 |
| #23761796 | 2 |
| #23761260 | 2 |
| C79×#1303 | 2 |
| #9176 | 79 |