Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 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×#14579683 | C2 | semidirect |
| 4. #23781913 | C2 | direct (N × H) |
| 5. C2×#19104668 | C2 | semidirect |
| 6. C2×#19104659 | C2 | semidirect |
| 7. C2×#19104655 | C2 | semidirect |
| 8. C2×C22⋊Q8×C163 | C2 | semidirect |
| 12. C2×#14579686 | C22 | semidirect |
| 14. C2×#14579683 | C22 | semidirect |
| 21. #19104668 | C22 | semidirect |
| 22. #19104659 | C22 | semidirect |
| 23. #19104655 | C22 | semidirect |
| 27. C22⋊Q8×C163 | C22 | semidirect |
| 42. C2×C163⋊C8 | D4 | semidirect |
| 76. C163⋊C8 | C2×D4 | semidirect |
| 118. C2×C163 | #468 | semidirect |
| 123. C163 | C2×#468 | semidirect |
| 127. C2×C22⋊Q8 | D163 | semidirect |
| 144. C22⋊Q8 | C2×D163 | semidirect |
| 243. C2 | #23781913 | 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×#14579683 | 2 |
| C2×#19104709 | 2 |
| #23781913 | 2 |
| C2×#19104668 | 2 |
| C2×#19104659 | 2 |
| C2×#19104655 | 2 |
| C2×C22⋊Q8×C163 | 2 |
| C2×#468 | 163 |