Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23782133 | C2 | semidirect |
| 3. #23781681 | C2 | semidirect |
| 4. C2×#19104661 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #23781426 | C2 | semidirect |
| 7. #344×C163 | C2 | semidirect |
| 11. #19104768 | C4 | semidirect |
| 13. #19104763 | C4 | semidirect |
| 37. C2×Dic326 | C2×C4 | semidirect |
| 39. C2×D652 | C2×C4 | semidirect |
| 64. M16×C163 | C2×C4 | semidirect |
| 129. C163 | #1906 | semidirect |
| 136. #344 | D163 | semidirect |
| 185. M16 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| #23782133 | 2 |
| #23781681 | 2 |
| C2×#19104661 | 2 |
| #23781638 | 2 |
| #23781426 | 2 |
| #344×C163 | 2 |
| #1906 | 163 |