Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. C22×#14579689 | C2 | semidirect |
| 4. C2×#19104658 | C2 | semidirect |
| 6. #23781420 | C2 | semidirect |
| 7. #391×C163 | C2 | semidirect |
| 125. C163 | #2015 | semidirect |
| 132. #391 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579689 | 2 |
| C22×#14579686 | 2 |
| C2×#19104723 | 2 |
| C2×#19104658 | 2 |
| C2×#19104655 | 2 |
| #23781420 | 2 |
| #391×C163 | 2 |
| #2015 | 163 |