Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
532 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19104768 | C2 | semidirect |
| 3. C22×Dic652 | C2 | semidirect |
| 4. #23782241 | C2 | semidirect |
| 5. #23782059 | C2 | semidirect |
| 6. #23782049 | C2 | semidirect |
| 7. #23782045 | C2 | semidirect |
| 8. #405×C163 | C2 | semidirect |
| 96. C163 | #3156 | semidirect |
| 105. #405 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104757 | 2 |
| C22×Dic652 | 2 |
| #23782241 | 2 |
| #23782059 | 2 |
| #23782049 | 2 |
| #23782045 | 2 |
| #405×C163 | 2 |
| #3156 | 163 |