Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #23781673 | C2 | semidirect |
| 4. C2×#19104653 | C2 | semidirect |
| 6. #23781430 | C2 | semidirect |
| 7. #424×C163 | C2 | semidirect |
| 100. C163 | #2046 | semidirect |
| 103. #424 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| #23781673 | 2 |
| #23781669 | 2 |
| C2×#19104653 | 2 |
| C2×#19104651 | 2 |
| #23781430 | 2 |
| #424×C163 | 2 |
| #2046 | 163 |