Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×Q8×D163 | C2 | semidirect |
| 2. C2×#19104768 | C2 | semidirect |
| 3. C2×#19104766 | C2 | semidirect |
| 5. #23781822 | C2 | semidirect |
| 6. #23781805 | C2 | semidirect |
| 7. #23781673 | C2 | semidirect |
| 8. #23781628 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 21. C2×Dic652 | C22 | semidirect |
| 22. C2×#14579689 | C22 | semidirect |
| 23. C2×#14579688 | C22 | semidirect |
| 24. C2×#14579686 | C22 | semidirect |
| 31. #19104658 | C22 | semidirect |
| 36. #103×C163 | C22 | semidirect |
| 44. C2×Dic326 | D4 | semidirect |
| 73. C2×Q8×C163 | D4 | semidirect |
| 127. C2×D163 | #137 | semidirect |
| 141. C163 | #3004 | semidirect |
| 150. #419 | D163 | semidirect |
| 177. #103 | C2×D163 | semidirect |
| 194. C2×Q8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D163 | 2 |
| C2×#19104768 | 2 |
| C2×#19104766 | 2 |
| #23782177 | 2 |
| #23781822 | 2 |
| #23781805 | 2 |
| #23781673 | 2 |
| #23781628 | 2 |
| #419×C163 | 2 |
| #3004 | 163 |