Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
190 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. C2×Dic1264 | C2 | semidirect |
| 3. #23761602 | C2 | semidirect |
| 4. #23761582 | C2 | semidirect |
| 71. C79 | #13698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1264 | 2 |
| #23765491 | 2 |
| #23761602 | 2 |
| #23761582 | 2 |
| C2×M64×C79 | 2 |
| #13698 | 79 |