Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104782 | C2 | semidirect |
| 2. C2×#19104760 | C2 | semidirect |
| 3. C22×#14579688 | C2 | semidirect |
| 4. #23782234 | C2 | semidirect |
| 5. #23781811 | C2 | semidirect |
| 6. #23781805 | C2 | semidirect |
| 7. #23781673 | C2 | semidirect |
| 8. #23781631 | C2 | semidirect |
| 9. #416×C163 | C2 | semidirect |
| 15. C2×#14579698 | C22 | semidirect |
| 18. C2×Q8×D163 | C22 | semidirect |
| 30. #19104658 | C22 | semidirect |
| 31. (C2×D163)⋊C8 | C22 | semidirect |
| 35. #103×C163 | C22 | semidirect |
| 36. #102×C163 | C22 | semidirect |
| 49. C2×Dic326 | D4 | semidirect |
| 72. #41×C163 | D4 | semidirect |
| 145. C163 | #3010 | semidirect |
| 154. #416 | D163 | semidirect |
| 180. #103 | C2×D163 | semidirect |
| 181. #102 | C2×D163 | semidirect |
| 191. #41 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| C2×#19104760 | 2 |
| C22×#14579688 | 2 |
| #23782234 | 2 |
| #23781811 | 2 |
| #23781805 | 2 |
| #23781673 | 2 |
| #23781631 | 2 |
| #416×C163 | 2 |
| #3010 | 163 |