Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 180. C79 | #7809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771362 | 2 |
| #23764942 | 2 |
| #23764871 | 2 |
| #23764810 | 2 |
| #23761225 | 2 |
| C79×#1271 | 2 |
| #7809 | 79 |