Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19104761 | C2 | semidirect |
| 2. #23782215 | C2 | semidirect |
| 3. #23782052 | C2 | semidirect |
| 4. #23782041 | C2 | semidirect |
| 5. #23782037 | C2 | semidirect |
| 6. C4×#14579683 | C2 | semidirect |
| 7. C2×#127×C163 | C2 | semidirect |
| 10. C2×#14579687 | C22 | semidirect |
| 11. C2×#14579684 | C22 | semidirect |
| 13. #19104735 | C22 | semidirect |
| 14. #19104732 | C22 | semidirect |
| 15. #19104723 | C22 | semidirect |
| 18. #19104646 | C22 | semidirect |
| 19. C4×C163⋊C8 | C22 | semidirect |
| 34. #14579683 | D4 | semidirect |
| 57. C163⋊C8 | C2×D4 | semidirect |
| 82. C4×C163 | AGL(1,ℤ/8) | semidirect |
| 90. C163 | #3151 | semidirect |
| 94. C2×#127 | D163 | semidirect |
| 174. C4 | #19104761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782215 | 2 |
| #23782052 | 2 |
| #23782041 | 2 |
| #23782037 | 2 |
| C4×#14579683 | 2 |
| C2×#127×C163 | 2 |
| #3151 | 163 |