Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19104734 | C2 | semidirect |
| 3. #23782010 | C2 | direct (N × H) |
| 4. C2×#19104657 | C2 | semidirect |
| 5. C2×#19104656 | C2 | semidirect |
| 6. C2×#19104655 | C2 | semidirect |
| 7. C2×C8×Dic163 | C2 | semidirect |
| 8. C2×#102×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 21. #19104657 | C22 | semidirect |
| 22. #19104656 | C22 | semidirect |
| 23. #19104655 | C22 | semidirect |
| 24. C8×Dic163 | C22 | semidirect |
| 28. #102×C163 | C22 | semidirect |
| 113. C2×C163 | #486 | semidirect |
| 118. C163 | C2×#486 | semidirect |
| 126. C2×#102 | D163 | semidirect |
| 146. #102 | C2×D163 | semidirect |
| 233. C2 | #23782010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104734 | 2 |
| C2×#19104731 | 2 |
| #23782010 | 2 |
| C2×#19104657 | 2 |
| C2×#19104656 | 2 |
| C2×#19104655 | 2 |
| C2×C8×Dic163 | 2 |
| C2×#102×C163 | 2 |
| C2×#486 | 163 |