Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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. #23782320 | C2 | semidirect |
| 3. #23782037 | C2 | semidirect |
| 4. #23781892 | C2 | semidirect |
| 5. #23781875 | C2 | semidirect |
| 6. #23781857 | C2 | semidirect |
| 7. #23781827 | C2 | semidirect |
| 8. #23781808 | C2 | semidirect |
| 9. C4×#14579686 | C2 | semidirect |
| 10. D4×C163⋊C8 | C2 | semidirect |
| 11. #550×C163 | C2 | semidirect |
| 52. #14579686 | D4 | semidirect |
| 129. C4×C163 | #135 | semidirect |
| 140. C163 | #3284 | semidirect |
| 143. #550 | D163 | semidirect |
| 272. 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 |
| #23782320 | 2 |
| #23782037 | 2 |
| #23781892 | 2 |
| #23781875 | 2 |
| #23781857 | 2 |
| #23781827 | 2 |
| #23781808 | 2 |
| C4×#14579686 | 2 |
| D4×C163⋊C8 | 2 |
| #550×C163 | 2 |
| #3284 | 163 |