Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104756 | C2 | semidirect |
| 2. #23782337 | C2 | semidirect |
| 3. #23782335 | C2 | semidirect |
| 4. #23782041 | C2 | semidirect |
| 5. #23781900 | C2 | semidirect |
| 6. #23781866 | C2 | semidirect |
| 7. #23781811 | C2 | semidirect |
| 8. #23781809 | C2 | semidirect |
| 9. C4×#14579689 | C2 | semidirect |
| 10. #23781730 | C2 | semidirect |
| 11. #460×C163 | C2 | semidirect |
| 58. #14579689 | D4 | semidirect |
| 130. C4×C163 | #135 | semidirect |
| 142. C163 | #3287 | semidirect |
| 150. #460 | D163 | semidirect |
| 276. C4 | #19104756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104756 | 2 |
| #23782337 | 2 |
| #23782335 | 2 |
| #23782041 | 2 |
| #23781900 | 2 |
| #23781866 | 2 |
| #23781811 | 2 |
| #23781809 | 2 |
| C4×#14579689 | 2 |
| #23781730 | 2 |
| #460×C163 | 2 |
| #3287 | 163 |