Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 2. C22×#14579686 | C2 | semidirect |
| 4. #23781887 | C2 | semidirect |
| 5. #23781865 | C2 | semidirect |
| 6. #23781692 | C2 | semidirect |
| 7. #23781669 | C2 | semidirect |
| 8. #23781659 | C2 | semidirect |
| 9. #519×C163 | C2 | semidirect |
| 13. C2×#14579689 | C22 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 23. C4⋊(C163⋊C8) | C22 | semidirect |
| 24. #19104658 | C22 | semidirect |
| 26. #19104655 | C22 | semidirect |
| 29. C4×Q8×C163 | C22 | semidirect |
| 55. C2×Q8×C163 | D4 | semidirect |
| 116. C163 | #3043 | semidirect |
| 121. #519 | D163 | semidirect |
| 142. C4×Q8 | C2×D163 | semidirect |
| 156. C2×Q8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| C22×#14579686 | 2 |
| #23782234 | 2 |
| #23781887 | 2 |
| #23781865 | 2 |
| #23781692 | 2 |
| #23781669 | 2 |
| #23781659 | 2 |
| #519×C163 | 2 |
| #3043 | 163 |