Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 14. #19098385 | C4 | semidirect |
| 126. C79 | #13114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098385 | 2 |
| #23764144 | 2 |
| #23763308 | 2 |
| #23761510 | 2 |
| #23761509 | 2 |
| #23761483 | 2 |
| C79×#1383 | 2 |
| #13114 | 79 |