Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
616 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 9. #19098502 | C4 | semidirect |
| 166. C79 | #9023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098502 | 2 |
| #23763488 | 2 |
| C2×#19098289 | 2 |
| #23761278 | 2 |
| C79×#2316 | 2 |
| #9023 | 79 |