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×#19104768 | C2 | semidirect |
| 2. C2×#19104755 | C2 | semidirect |
| 3. C22×#14579687 | C2 | semidirect |
| 4. #23782236 | C2 | semidirect |
| 5. #23782232 | C2 | semidirect |
| 6. #23782056 | C2 | semidirect |
| 7. #23782053 | C2 | semidirect |
| 8. #23782048 | C2 | semidirect |
| 9. #23782036 | C2 | semidirect |
| 10. #23781623 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 16. C2×Dic652 | C22 | semidirect |
| 17. C2×#14579689 | C22 | semidirect |
| 18. C2×#14579688 | C22 | semidirect |
| 22. C2×#14579687 | C22 | semidirect |
| 23. C2×#14579686 | C22 | semidirect |
| 24. C2×#14579684 | C22 | semidirect |
| 26. #19104733 | C22 | semidirect |
| 29. #19104722 | C22 | semidirect |
| 35. #19104645 | C22 | semidirect |
| 36. C8×Dic163 | C22 | semidirect |
| 63. C2×C163⋊C8 | D4 | semidirect |
| 86. M16×C163 | D4 | semidirect |
| 148. C163 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 226. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104755 | 2 |
| C22×#14579687 | 2 |
| #23782236 | 2 |
| #23782232 | 2 |
| #23782056 | 2 |
| #23782053 | 2 |
| #23782048 | 2 |
| #23782036 | 2 |
| #23781623 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3154 | 163 |