Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14579689 | C2 | semidirect |
| 2. C22×#14579687 | C2 | semidirect |
| 3. C2×#19104714 | C2 | semidirect |
| 4. #23781827 | C2 | direct (N × H) |
| 5. C2×#19104659 | C2 | semidirect |
| 6. C2×#19104656 | C2 | semidirect |
| 7. C2×C22⋊(C163⋊C8) | C2 | semidirect |
| 11. C2×#14579689 | C22 | semidirect |
| 13. C2×#14579687 | C22 | semidirect |
| 17. #19104714 | C22 | semidirect |
| 21. #19104659 | C22 | semidirect |
| 22. #19104656 | C22 | semidirect |
| 23. C22⋊(C163⋊C8) | C22 | semidirect |
| 131. C2×C163 | #452 | semidirect |
| 135. C163 | C2×#452 | semidirect |
| 267. C2 | #23781827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579689 | 2 |
| C22×#14579687 | 2 |
| C2×#19104714 | 2 |
| #23781827 | 2 |
| C2×#19104659 | 2 |
| C2×#19104656 | 2 |
| C2×C22⋊(C163⋊C8) | 2 |
| C22×#41×C163 | 2 |
| C2×#452 | 163 |