Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1830 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1830 conjugacy classes of subgroups — too many to draw. Only its 667 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. #23769365 | C2 | direct (N × H) |
| 92. C2×C79 | #2645 | semidirect |
| 102. C79 | C2×#2645 | semidirect |
| 187. C2 | #23769365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769365 | 2 |
| C2×C79⋊#401 | 2 |
| C2×#19098504 | 2 |
| C2×#19098469 | 2 |
| C2×#19098461 | 2 |
| C2×#376×C79 | 2 |
| C2×#2645 | 79 |