Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23761600 | C2 | semidirect |
| 4. #23761582 | C2 | semidirect |
| 56. C22×C79 | Q64 | semidirect |
| 73. C79 | #13695 | semidirect |
| 124. C22 | Dic1264 | 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 |
| #23761600 | 2 |
| #23761582 | 2 |
| C22×C32×C79 | 2 |
| #13695 | 79 |