Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104755 | C2 | semidirect |
| 2. #23782336 | C2 | semidirect |
| 3. #23782041 | C2 | semidirect |
| 4. #23781899 | C2 | semidirect |
| 5. #23781865 | C2 | semidirect |
| 6. #23781862 | C2 | semidirect |
| 7. #23781810 | C2 | semidirect |
| 8. #23781808 | C2 | semidirect |
| 9. C4×#14579689 | C2 | semidirect |
| 10. D4×C163⋊C8 | C2 | semidirect |
| 11. #550×C163 | C2 | semidirect |
| 51. #14579689 | D4 | semidirect |
| 131. C4×C163 | #135 | semidirect |
| 142. C163 | #3287 | semidirect |
| 146. #550 | D163 | semidirect |
| 276. C4 | #19104755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| #23782336 | 2 |
| #23782041 | 2 |
| #23781899 | 2 |
| #23781865 | 2 |
| #23781862 | 2 |
| #23781810 | 2 |
| #23781808 | 2 |
| C4×#14579689 | 2 |
| D4×C163⋊C8 | 2 |
| #550×C163 | 2 |
| #3287 | 163 |