Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1266 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 10. C2×C4×Dic158 | C4 | semidirect |
| 11. C2×#14579126 | C4 | semidirect |
| 142. C79 | #20691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099040 | 2 |
| #23765985 | 2 |
| #23763477 | 2 |
| #23763476 | 2 |
| #23763475 | 2 |
| #23763131 | 2 |
| C79×#1820 | 2 |
| #20691 | 79 |