Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 8. C22×#11929614 | C4 | semidirect |
| 15. C2×#14579094 | C4 | semidirect |
| 17. C2×#14579085 | C4 | semidirect |
| 18. C2×#14579084 | C4 | semidirect |
| 227. C79 | #9784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098802 | 2 |
| #23764385 | 2 |
| #23763423 | 2 |
| #23763178 | 2 |
| #23761972 | 2 |
| #23761971 | 2 |
| C79×#1996 | 2 |
| #9784 | 79 |