Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×C42×D163 | C2 | semidirect |
| 3. C2×#19104663 | C2 | semidirect |
| 4. C2×#19104661 | C2 | semidirect |
| 5. #23781628 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 13. #19104715 | C4 | semidirect |
| 14. #19104710 | C4 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 34. C2×D652 | C2×C4 | semidirect |
| 55. C4×Dic163 | D4 | semidirect |
| 61. C4⋊C4×C163 | C2×C4 | semidirect |
| 65. C42×C163 | D4 | semidirect |
| 113. C2×D163 | #104 | semidirect |
| 129. C163 | #1896 | semidirect |
| 137. #339 | D163 | semidirect |
| 186. C4⋊C4 | C4×D163 | semidirect |
| 195. C42 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782177 | 2 |
| C2×C42×D163 | 2 |
| C2×#19104663 | 2 |
| C2×#19104661 | 2 |
| #23781628 | 2 |
| #23781424 | 2 |
| #339×C163 | 2 |
| #1896 | 163 |