Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 762 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. C2×#19104780 | C2 | semidirect |
| 2. #23782463 | C2 | semidirect |
| 3. #23781842 | C2 | semidirect |
| 4. #23781832 | C2 | semidirect |
| 5. #23781683 | C2 | semidirect |
| 6. C2×#19104652 | C2 | semidirect |
| 7. #535×C163 | C2 | semidirect |
| 15. #19104766 | C22 | semidirect |
| 17. #19104761 | C22 | semidirect |
| 20. C2×#14579683 | C22 | semidirect |
| 21. #19104663 | C22 | semidirect |
| 22. #19104652 | C22 | semidirect |
| 23. C2×#41×C163 | C22 | semidirect |
| 25. #127×C163 | C22 | semidirect |
| 26. #124×C163 | C22 | semidirect |
| 29. #117×C163 | C22 | semidirect |
| 33. #14579699 | D4 | semidirect |
| 37. C2×Dic326 | D4 | semidirect |
| 38. C2×D652 | D4 | semidirect |
| 52. #14579683 | C23 | semidirect |
| 57. C2×Q8×C163 | C23 | semidirect |
| 64. C2×D4×C163 | C23 | semidirect |
| 70. C42×C163 | C23 | semidirect |
| 131. C163 | #3019 | semidirect |
| 135. #535 | D163 | semidirect |
| 145. C2×#41 | C2×D163 | semidirect |
| 155. #127 | C2×D163 | semidirect |
| 156. #124 | C2×D163 | semidirect |
| 159. #117 | C2×D163 | semidirect |
| 173. C2×Q8 | C22×D163 | semidirect |
| 187. C2×D4 | C22×D163 | semidirect |
| 202. C42 | C22×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| #23782463 | 2 |
| #23781842 | 2 |
| #23781832 | 2 |
| #23781683 | 2 |
| C2×#19104652 | 2 |
| #535×C163 | 2 |
| #3019 | 163 |