Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23761425 | C2 | semidirect |
| 4. #23761401 | C2 | semidirect |
| 6. C2×#14579153 | C4 | semidirect |
| 8. #19098499 | C4 | semidirect |
| 11. #19098488 | C4 | semidirect |
| 16. #19098431 | C4 | semidirect |
| 189. C79 | #11827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769268 | 2 |
| #23763388 | 2 |
| #23761425 | 2 |
| #23761401 | 2 |
| C79×#1465 | 2 |
| #11827 | 79 |