Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#19104700 | C2 | semidirect |
| 4. #23781762 | C2 | direct (N × H) |
| 5. C2×#19104668 | C2 | semidirect |
| 6. C2×#19104660 | C2 | semidirect |
| 7. C2×#19104645 | C2 | semidirect |
| 11. C2×#14579687 | C4 | semidirect |
| 15. #19104700 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104660 | C22 | semidirect |
| 25. #19104645 | C22 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 40. #14579687 | C2×C4 | semidirect |
| 41. C2×C163⋊C8 | C2×C4 | semidirect |
| 63. Dic326 | C22×C4 | semidirect |
| 73. C163⋊C8 | C22×C4 | semidirect |
| 106. C2×C163 | #440 | semidirect |
| 110. C163 | C2×#440 | semidirect |
| 217. C2 | #23781762 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579687 | 2 |
| C2×#19104700 | 2 |
| C2×D4×Dic163 | 2 |
| #23781762 | 2 |
| C2×#19104668 | 2 |
| C2×#19104660 | 2 |
| C2×#19104645 | 2 |
| C2×#102×C163 | 2 |
| C2×#440 | 163 |