Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 80. C2×Dic158 | Q16 | semidirect |
| 192. C79 | #10252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773201 | 2 |
| #23768616 | 2 |
| #23762081 | 2 |
| #23761899 | 2 |
| #23761794 | 2 |
| #23761302 | 2 |
| C79×#3209 | 2 |
| #10252 | 79 |