Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 23. #14579159 | C8 | semidirect |
| 144. C79 | #9100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766116 | 2 |
| #23761796 | 2 |
| #23761724 | 2 |
| #23761228 | 2 |
| C79×#2982 | 2 |
| #9100 | 79 |