Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#19104766 | C2 | semidirect |
| 3. C4×#14579699 | C2 | semidirect |
| 4. #23781884 | C2 | semidirect |
| 5. #23781877 | C2 | semidirect |
| 6. #23781689 | C2 | semidirect |
| 7. #23781674 | C2 | semidirect |
| 8. #23781670 | C2 | semidirect |
| 9. C2×#124×C163 | C2 | semidirect |
| 13. C2×#14579689 | C22 | semidirect |
| 15. C2×#14579686 | C22 | semidirect |
| 19. C4×Dic326 | C22 | semidirect |
| 20. C4×D652 | C22 | semidirect |
| 25. C4⋊(C163⋊C8) | C22 | semidirect |
| 26. #19104659 | C22 | semidirect |
| 125. C163 | #3040 | semidirect |
| 129. C2×#124 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| C2×#19104761 | 2 |
| C4×#14579699 | 2 |
| #23781884 | 2 |
| #23781877 | 2 |
| #23781689 | 2 |
| #23781674 | 2 |
| #23781670 | 2 |
| C2×#124×C163 | 2 |
| #3040 | 163 |