Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 2. C22×#14579689 | C2 | semidirect |
| 3. C22×#14579686 | C2 | semidirect |
| 4. #23781825 | C2 | direct (N × H) |
| 5. C2×#19104658 | C2 | semidirect |
| 6. C2×#19104655 | C2 | semidirect |
| 7. C2×C22⋊(C163⋊C8) | C2 | semidirect |
| 8. C2×C22⋊Q8×C163 | C2 | semidirect |
| 18. C2×#14579689 | C22 | semidirect |
| 20. C2×#14579686 | C22 | semidirect |
| 23. #19104658 | C22 | semidirect |
| 24. #19104655 | C22 | semidirect |
| 25. C22⋊(C163⋊C8) | C22 | semidirect |
| 29. C22⋊Q8×C163 | C22 | semidirect |
| 130. C2×C163 | #452 | semidirect |
| 135. C163 | C2×#452 | semidirect |
| 140. C2×C22⋊Q8 | D163 | semidirect |
| 162. C22⋊Q8 | C2×D163 | semidirect |
| 267. C2 | #23781825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C22×#14579689 | 2 |
| C22×#14579686 | 2 |
| #23781825 | 2 |
| C2×#19104658 | 2 |
| C2×#19104655 | 2 |
| C2×C22⋊(C163⋊C8) | 2 |
| C2×C22⋊Q8×C163 | 2 |
| C2×#452 | 163 |