Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
830 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 1. #23763545 | C2 | semidirect |
| 53. C79 | #20773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763545 | 2 |
| #23763094 | 2 |
| C2×#376×C79 | 2 |
| #20773 | 79 |