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×#19104783 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. C22×#14579686 | C2 | semidirect |
| 4. #23782234 | C2 | semidirect |
| 5. #23781813 | C2 | semidirect |
| 6. #23781805 | C2 | semidirect |
| 7. #23781659 | C2 | semidirect |
| 8. #23781633 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 13. C2×#14579700 | C22 | semidirect |
| 18. C2×Q8×D163 | C22 | semidirect |
| 30. #19104658 | C22 | semidirect |
| 31. #19104655 | C22 | semidirect |
| 32. (C2×D163)⋊C8 | C22 | semidirect |
| 36. #103×C163 | C22 | semidirect |
| 45. #14579699 | D4 | semidirect |
| 74. C2×Q8×C163 | D4 | semidirect |
| 145. C163 | #3010 | semidirect |
| 153. #419 | D163 | semidirect |
| 180. #103 | C2×D163 | semidirect |
| 200. C2×Q8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| C2×#19104763 | 2 |
| C22×#14579686 | 2 |
| #23782234 | 2 |
| #23781813 | 2 |
| #23781805 | 2 |
| #23781659 | 2 |
| #23781633 | 2 |
| #419×C163 | 2 |
| #3010 | 163 |