Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#19104765 | C2 | semidirect |
| 2. C2×#19104714 | C2 | semidirect |
| 3. #23781827 | C2 | semidirect |
| 4. #23781821 | C2 | semidirect |
| 5. #23781816 | C2 | semidirect |
| 6. #23781666 | C2 | semidirect |
| 7. #23781629 | C2 | semidirect |
| 9. C22×Dic326 | C22 | semidirect |
| 11. C2×#14579689 | C22 | semidirect |
| 12. C2×#14579687 | C22 | semidirect |
| 13. C2×#14579683 | C22 | semidirect |
| 17. #19104714 | C22 | semidirect |
| 18. C2×C4⋊Dic163 | C22 | semidirect |
| 21. #19104659 | C22 | semidirect |
| 22. #19104656 | C22 | semidirect |
| 24. C22⋊(C163⋊C8) | C22 | semidirect |
| 130. C22×C163 | #137 | semidirect |
| 146. C163 | #3007 | semidirect |
| 277. C22 | #19104765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104714 | 2 |
| #23781827 | 2 |
| #23781821 | 2 |
| #23781816 | 2 |
| #23781666 | 2 |
| #23781629 | 2 |
| C22×#41×C163 | 2 |
| #3007 | 163 |