Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782501 | C2 | semidirect |
| 2. #23782463 | C2 | semidirect |
| 3. #23781847 | C2 | semidirect |
| 4. #23781842 | C2 | semidirect |
| 5. #23781837 | C2 | semidirect |
| 6. #23781832 | C2 | semidirect |
| 7. C2×#19104663 | C2 | semidirect |
| 8. #23781649 | C2 | semidirect |
| 9. #532×C163 | C2 | semidirect |
| 18. #19104766 | C22 | semidirect |
| 20. #19104761 | C22 | semidirect |
| 23. C2×#14579683 | C22 | semidirect |
| 24. #19104663 | C22 | semidirect |
| 25. #19104663 | C22 | semidirect |
| 26. #19104654 | C22 | semidirect |
| 27. #19104652 | C22 | semidirect |
| 29. C2×#41×C163 | C22 | semidirect |
| 30. C4⋊Q8×C163 | C22 | semidirect |
| 31. #127×C163 | C22 | semidirect |
| 32. #124×C163 | C22 | semidirect |
| 33. #124×C163 | C22 | semidirect |
| 36. C2×C42×C163 | C22 | semidirect |
| 43. #14579699 | D4 | semidirect |
| 48. C2×Dic326 | D4 | semidirect |
| 51. C2×D652 | D4 | semidirect |
| 150. C163 | #3018 | semidirect |
| 154. #532 | D163 | semidirect |
| 170. C2×#41 | C2×D163 | semidirect |
| 177. C4⋊Q8 | C2×D163 | semidirect |
| 178. #127 | C2×D163 | semidirect |
| 179. #124 | C2×D163 | semidirect |
| 180. #124 | C2×D163 | semidirect |
| 183. C2×C42 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| #23782463 | 2 |
| #23781847 | 2 |
| #23781842 | 2 |
| #23781837 | 2 |
| #23781832 | 2 |
| C2×#19104663 | 2 |
| #23781649 | 2 |
| #532×C163 | 2 |
| #3018 | 163 |