Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19104758 | C2 | semidirect |
| 2. C2×D8×D163 | C2 | semidirect |
| 3. #23782102 | C2 | direct (N × H) |
| 4. C2×#19104678 | C2 | semidirect |
| 5. C2×D2608 | C2 | semidirect |
| 6. C2×#19104676 | C2 | semidirect |
| 7. C2×#19104674 | C2 | semidirect |
| 8. C2×SD32×C163 | C2 | semidirect |
| 12. #19104758 | C22 | semidirect |
| 15. C2×D1304 | C22 | semidirect |
| 18. D8×D163 | C22 | semidirect |
| 20. #19104678 | C22 | semidirect |
| 21. D2608 | C22 | semidirect |
| 22. #19104676 | C22 | semidirect |
| 23. #19104674 | C22 | semidirect |
| 24. C2×C163⋊C16 | C22 | semidirect |
| 25. C2×Q16×C163 | C22 | semidirect |
| 27. SD32×C163 | C22 | semidirect |
| 28. C2×C16×C163 | C22 | semidirect |
| 44. D1304 | C23 | semidirect |
| 49. C163⋊C16 | C23 | semidirect |
| 53. Q16×C163 | C23 | semidirect |
| 57. C16×C163 | C23 | semidirect |
| 98. C2×C163 | #509 | semidirect |
| 103. C163 | C2×#509 | semidirect |
| 109. C2×SD32 | D163 | semidirect |
| 117. C2×Q16 | C2×D163 | semidirect |
| 127. SD32 | C2×D163 | semidirect |
| 132. C2×C16 | C2×D163 | semidirect |
| 147. Q16 | C22×D163 | semidirect |
| 161. C16 | C22×D163 | semidirect |
| 205. C2 | #23782102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×D8×D163 | 2 |
| #23782102 | 2 |
| C2×#19104678 | 2 |
| C2×D2608 | 2 |
| C2×#19104676 | 2 |
| C2×#19104674 | 2 |
| C2×SD32×C163 | 2 |
| C2×#509 | 163 |