Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
812 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. #23763491 | C2 | semidirect |
| 4. #23761280 | C2 | semidirect |
| 11. #19098499 | C4 | semidirect |
| 27. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 40. C79⋊#95 | C2×C4 | semidirect |
| 196. C79 | #9021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098499 | 2 |
| #23766014 | 2 |
| #23763491 | 2 |
| #23761280 | 2 |
| C2×#323×C79 | 2 |
| #9021 | 79 |