Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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×#19104760 | C2 | semidirect |
| 2. #23782229 | C2 | semidirect |
| 3. #23781838 | C2 | semidirect |
| 4. #23781833 | C2 | semidirect |
| 5. #23781682 | C2 | semidirect |
| 6. #23781649 | C2 | semidirect |
| 7. #585×C163 | C2 | semidirect |
| 8. C22×D652 | C22 | semidirect |
| 10. #19104760 | C22 | semidirect |
| 13. C2×#14579683 | C22 | semidirect |
| 14. #19104731 | C22 | semidirect |
| 15. #19104724 | C22 | semidirect |
| 18. #19104694 | C22 | semidirect |
| 19. #19104662 | C22 | semidirect |
| 20. #19104654 | C22 | semidirect |
| 21. #19104652 | C22 | semidirect |
| 23. 2−1+4×C163 | C22 | semidirect |
| 26. H(5,𝔽2)×C163 | C22 | semidirect |
| 56. #41×C163 | D4 | semidirect |
| 60. C2×Q8×C163 | D4 | semidirect |
| 68. C2×D4×C163 | D4 | semidirect |
| 134. C163 | #3021 | semidirect |
| 136. #585 | D163 | semidirect |
| 144. 2−1+4 | C2×D163 | semidirect |
| 147. H(5,𝔽2) | C2×D163 | semidirect |
| 177. #41 | C22⋊D163 | semidirect |
| 181. C2×Q8 | C22⋊D163 | semidirect |
| 194. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| #23782229 | 2 |
| #23781838 | 2 |
| #23781833 | 2 |
| #23781682 | 2 |
| #23781649 | 2 |
| #585×C163 | 2 |
| #3021 | 163 |