Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 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. #23782463 | C2 | semidirect |
| 2. #23782232 | C2 | semidirect |
| 3. #23781843 | C2 | semidirect |
| 4. #23781833 | C2 | semidirect |
| 5. #23781682 | C2 | semidirect |
| 6. C2×#19104652 | C2 | semidirect |
| 7. C2×H(5,𝔽2)×C163 | C2 | semidirect |
| 8. C2×#14579699 | C22 | semidirect |
| 10. #19104765 | C22 | semidirect |
| 12. #19104760 | C22 | semidirect |
| 14. C2×#14579683 | C22 | semidirect |
| 15. #19104731 | C22 | semidirect |
| 16. #19104722 | C22 | semidirect |
| 19. #19104694 | C22 | semidirect |
| 20. #19104662 | C22 | semidirect |
| 21. #19104652 | C22 | semidirect |
| 32. C2×Dic326 | C23 | semidirect |
| 33. C2×D652 | C23 | semidirect |
| 42. #14579683 | C23 | semidirect |
| 47. C4×Dic163 | C23 | semidirect |
| 54. #41×C163 | D4 | semidirect |
| 56. C2×Q8×C163 | D4 | semidirect |
| 66. C2×D4×C163 | D4 | semidirect |
| 131. C163 | #3019 | semidirect |
| 133. C2×H(5,𝔽2) | D163 | semidirect |
| 170. #41 | C22⋊D163 | semidirect |
| 173. C2×Q8 | C22⋊D163 | semidirect |
| 186. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| #23782232 | 2 |
| #23781843 | 2 |
| #23781833 | 2 |
| #23781682 | 2 |
| C2×#19104652 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| #3019 | 163 |