Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 382 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. C2×#19104649 | C2 | semidirect |
| 3. #23781544 | C2 | semidirect |
| 4. #23781432 | C2 | semidirect |
| 5. #385×C163 | C2 | semidirect |
| 48. C22⋊C4×C163 | D4 | semidirect |
| 116. C163 | #2044 | semidirect |
| 121. #385 | D163 | semidirect |
| 165. C22⋊C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782227 | 2 |
| C2×#19104649 | 2 |
| #23781544 | 2 |
| #23781432 | 2 |
| #385×C163 | 2 |
| #2044 | 163 |