Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#19104766 | C2 | semidirect |
| 3. C2×#19104757 | C2 | semidirect |
| 4. #23782246 | C2 | semidirect |
| 5. #23781830 | C2 | semidirect |
| 6. #23781822 | C2 | semidirect |
| 7. #23781813 | C2 | semidirect |
| 8. #23781805 | C2 | semidirect |
| 9. #23781664 | C2 | semidirect |
| 10. #23781631 | C2 | semidirect |
| 11. C2×#103×C163 | C2 | semidirect |
| 54. #14579699 | D4 | semidirect |
| 88. C2×Q8×C163 | D4 | semidirect |
| 169. C163 | #3013 | semidirect |
| 180. C2×#103 | D163 | semidirect |
| 234. 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×#19104766 | 2 |
| C2×#19104757 | 2 |
| #23782246 | 2 |
| #23781830 | 2 |
| #23781822 | 2 |
| #23781813 | 2 |
| #23781805 | 2 |
| #23781664 | 2 |
| #23781631 | 2 |
| C2×#103×C163 | 2 |
| #3013 | 163 |