Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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×#19104765 | C2 | semidirect |
| 3. C2×#19104723 | C2 | semidirect |
| 4. #23781887 | C2 | semidirect |
| 5. #23781880 | C2 | semidirect |
| 6. #23781689 | C2 | semidirect |
| 7. #23781673 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. C4×#41×C163 | C2 | semidirect |
| 14. C2×#14579689 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 24. C4⋊(C163⋊C8) | C22 | semidirect |
| 25. #19104658 | C22 | semidirect |
| 28. C4×Q8×C163 | C22 | semidirect |
| 30. C4×D4×C163 | C22 | semidirect |
| 125. C163 | #3040 | semidirect |
| 130. C4×#41 | D163 | semidirect |
| 150. C4×Q8 | C2×D163 | semidirect |
| 152. C4×D4 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104760 | 2 |
| C2×#19104723 | 2 |
| #23781887 | 2 |
| #23781880 | 2 |
| #23781689 | 2 |
| #23781673 | 2 |
| #23781669 | 2 |
| C4×#41×C163 | 2 |
| #3040 | 163 |