Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
724 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 724 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. #23782211 | C2 | semidirect |
| 3. #23781848 | C2 | semidirect |
| 4. #23781843 | C2 | semidirect |
| 5. #23781838 | C2 | semidirect |
| 6. #23781833 | C2 | semidirect |
| 7. C2×#19104662 | C2 | semidirect |
| 8. #23781649 | C2 | semidirect |
| 9. #585×C163 | C2 | semidirect |
| 10. C2×#14579699 | C22 | semidirect |
| 12. #19104765 | C22 | semidirect |
| 14. #19104760 | C22 | semidirect |
| 16. C2×#14579683 | C22 | semidirect |
| 17. #19104733 | C22 | semidirect |
| 18. #19104731 | C22 | semidirect |
| 19. #19104724 | C22 | semidirect |
| 20. #19104722 | C22 | semidirect |
| 23. C2×C4×Dic163 | C22 | semidirect |
| 24. #19104662 | C22 | semidirect |
| 25. #19104662 | C22 | semidirect |
| 26. #19104654 | C22 | semidirect |
| 27. #19104652 | C22 | semidirect |
| 68. #41×C163 | D4 | semidirect |
| 72. C2×Q8×C163 | D4 | semidirect |
| 80. C2×D4×C163 | D4 | semidirect |
| 150. C163 | #3018 | semidirect |
| 152. #585 | D163 | semidirect |
| 200. #41 | C22⋊D163 | semidirect |
| 205. C2×Q8 | C22⋊D163 | semidirect |
| 216. 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 |
| #23782211 | 2 |
| #23781848 | 2 |
| #23781843 | 2 |
| #23781838 | 2 |
| #23781833 | 2 |
| C2×#19104662 | 2 |
| #23781649 | 2 |
| #585×C163 | 2 |
| #3018 | 163 |