Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×C4×Dic326 | C2 | semidirect |
| 4. #23781888 | C2 | semidirect |
| 5. #23781876 | C2 | semidirect |
| 6. #23781866 | C2 | semidirect |
| 7. #23781667 | C2 | semidirect |
| 8. #423×C163 | C2 | semidirect |
| 38. C2×Dic326 | D4 | semidirect |
| 109. C4×C163 | #137 | semidirect |
| 120. C163 | #3037 | semidirect |
| 128. #423 | D163 | semidirect |
| 233. C4 | #19104768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| #23782215 | 2 |
| C2×C4×Dic326 | 2 |
| #23781888 | 2 |
| #23781876 | 2 |
| #23781866 | 2 |
| #23781667 | 2 |
| #423×C163 | 2 |
| #3037 | 163 |