Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 18. #19098361 | C4 | semidirect |
| 172. C79 | #12631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766116 | 2 |
| C2×#19098361 | 2 |
| C4×#14579080 | 2 |
| #23761526 | 2 |
| C4×#101×C79 | 2 |
| #12631 | 79 |