Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#19104766 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. C2×#19104757 | C2 | semidirect |
| 4. #23782239 | C2 | semidirect |
| 5. #23782232 | C2 | semidirect |
| 6. #23782056 | C2 | semidirect |
| 7. #23782051 | C2 | semidirect |
| 8. #23782046 | C2 | semidirect |
| 9. #23782036 | C2 | semidirect |
| 10. #23781620 | C2 | semidirect |
| 11. C22×SD16×C163 | C2 | semidirect |
| 17. C2×Dic652 | C22 | semidirect |
| 18. C2×#14579689 | C22 | semidirect |
| 19. C2×#14579688 | C22 | semidirect |
| 20. C2×#14579688 | C22 | semidirect |
| 22. C2×#14579686 | C22 | semidirect |
| 23. C2×D1304 | C22 | semidirect |
| 26. #19104733 | C22 | semidirect |
| 28. #19104724 | C22 | semidirect |
| 35. #19104645 | C22 | semidirect |
| 36. C8×Dic163 | C22 | semidirect |
| 64. #14579683 | D4 | semidirect |
| 85. C2×C8×C163 | D4 | semidirect |
| 148. C163 | #3154 | semidirect |
| 153. C22×SD16 | D163 | semidirect |
| 228. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| C2×#19104761 | 2 |
| C2×#19104757 | 2 |
| #23782239 | 2 |
| #23782232 | 2 |
| #23782056 | 2 |
| #23782051 | 2 |
| #23782046 | 2 |
| #23782036 | 2 |
| #23781620 | 2 |
| C22×SD16×C163 | 2 |
| #3154 | 163 |