Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14579687 | C2 | semidirect |
| 3. #23782142 | C2 | semidirect |
| 4. #23781884 | C2 | semidirect |
| 5. #23781862 | C2 | semidirect |
| 6. #23781692 | C2 | semidirect |
| 7. #23781670 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 12. C2×#14579689 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 18. C4×Dic326 | C22 | semidirect |
| 22. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. #19104659 | C22 | semidirect |
| 25. #19104656 | C22 | semidirect |
| 35. C2×Dic326 | D4 | semidirect |
| 116. C163 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C22×#14579687 | 2 |
| #23782142 | 2 |
| #23781884 | 2 |
| #23781862 | 2 |
| #23781692 | 2 |
| #23781670 | 2 |
| #23781661 | 2 |
| #535×C163 | 2 |
| #3043 | 163 |