Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23761286 | C2 | semidirect |
| 4. #23761253 | C2 | semidirect |
| 10. #19098429 | C4 | semidirect |
| 11. #19098426 | C4 | semidirect |
| 14. C4×C4⋊Dic79 | C4 | semidirect |
| 15. C4×C22⋊Dic79 | C4 | semidirect |
| 178. C79 | #8778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766373 | 2 |
| #23761738 | 2 |
| #23761286 | 2 |
| #23761253 | 2 |
| C4×#99×C79 | 2 |
| #8778 | 79 |