Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14579687 | C2 | semidirect |
| 3. C2×#19104723 | C2 | semidirect |
| 4. #23781880 | C2 | direct (N × H) |
| 5. C2×C4⋊(C163⋊C8) | C2 | semidirect |
| 6. C2×#19104658 | C2 | semidirect |
| 7. C2×#19104655 | C2 | semidirect |
| 8. C2×C4×D4×C163 | C2 | semidirect |
| 12. C2×#14579687 | C22 | semidirect |
| 18. #19104723 | C22 | semidirect |
| 21. C4⋊(C163⋊C8) | C22 | semidirect |
| 22. #19104658 | C22 | semidirect |
| 23. #19104655 | C22 | semidirect |
| 27. C4×D4×C163 | C22 | semidirect |
| 118. C2×C163 | #463 | semidirect |
| 123. C163 | C2×#463 | semidirect |
| 128. C2×C4×D4 | D163 | semidirect |
| 146. C4×D4 | C2×D163 | semidirect |
| 243. C2 | #23781880 | 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 |
| C22×#14579684 | 2 |
| C2×#19104723 | 2 |
| #23781880 | 2 |
| C2×C4⋊(C163⋊C8) | 2 |
| C2×#19104658 | 2 |
| C2×#19104655 | 2 |
| C2×C4×D4×C163 | 2 |
| C2×#463 | 163 |