Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23781688 | C2 | semidirect |
| 3. C2×#19104663 | C2 | semidirect |
| 4. C2×#19104662 | C2 | semidirect |
| 5. C2×#19104661 | C2 | semidirect |
| 6. #23781511 | C2 | semidirect |
| 7. C2×#104×C163 | C2 | semidirect |
| 10. #19104733 | C4 | semidirect |
| 11. #19104731 | C4 | semidirect |
| 12. #19104724 | C4 | semidirect |
| 13. #19104722 | C4 | semidirect |
| 48. C4×Dic163 | D4 | semidirect |
| 63. C42×C163 | D4 | semidirect |
| 125. C163 | #1963 | semidirect |
| 132. C2×#104 | D163 | semidirect |
| 189. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782211 | 2 |
| #23781688 | 2 |
| C2×#19104663 | 2 |
| C2×#19104662 | 2 |
| C2×#19104661 | 2 |
| #23781511 | 2 |
| C2×#104×C163 | 2 |
| #1963 | 163 |