Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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. Dic1264 | C4 | semidirect |
| 60. C79 | #13653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1264 | 2 |
| C4×Dic632 | 2 |
| #23761602 | 2 |
| #23761582 | 2 |
| C79×#1397 | 2 |
| #13653 | 79 |