Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 7. C2×C4×Dic158 | C4 | semidirect |
| 9. #19098468 | C4 | semidirect |
| 15. #19098432 | C4 | semidirect |
| 17. #19098409 | C4 | semidirect |
| 68. C2×Dic158 | C4⋊C4 | semidirect |
| 91. C4×Dic79 | C4⋊C4 | semidirect |
| 221. C79 | #12800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766112 | 2 |
| C2×#19098357 | 2 |
| #23763388 | 2 |
| #23761524 | 2 |
| C79×#1799 | 2 |
| #12800 | 79 |