Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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. C22×#14579686 | C2 | semidirect |
| 2. C22×C8×D163 | C2 | semidirect |
| 3. C2×#19104711 | C2 | semidirect |
| 5. #23781897 | C2 | direct (N × H) |
| 6. C2×#19104666 | C2 | semidirect |
| 7. C2×#19104657 | C2 | semidirect |
| 8. C2×#103×C163 | C2 | semidirect |
| 13. C2×#14579686 | C22 | semidirect |
| 16. C2×C8×D163 | C22 | semidirect |
| 18. #19104711 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104657 | C22 | semidirect |
| 30. #103×C163 | C22 | semidirect |
| 46. C2×C163⋊C8 | D4 | semidirect |
| 71. C22×D163 | SD16 | semidirect |
| 84. C163⋊C8 | C2×D4 | semidirect |
| 109. C2×D163 | C2×SD16 | semidirect |
| 117. C2×C163 | #465 | semidirect |
| 123. C163 | C2×#465 | semidirect |
| 131. C2×#103 | D163 | semidirect |
| 153. #103 | C2×D163 | semidirect |
| 243. C2 | #23781897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579686 | 2 |
| C22×C8×D163 | 2 |
| C2×#19104711 | 2 |
| C2×#19104710 | 2 |
| #23781897 | 2 |
| C2×#19104666 | 2 |
| C2×#19104657 | 2 |
| C2×#103×C163 | 2 |
| C2×#465 | 163 |