Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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. #99×D163 | C2 | semidirect |
| 3. #23781459 | C2 | semidirect |
| 4. #23781458 | C2 | semidirect |
| 5. #353×C163 | C2 | semidirect |
| 6. C2×#14579698 | C4 | semidirect |
| 8. #19104731 | C4 | semidirect |
| 9. #19104723 | C4 | semidirect |
| 13. #19104692 | C4 | semidirect |
| 21. C2×Dic326 | C2×C4 | semidirect |
| 36. C4×Dic163 | C2×C4 | semidirect |
| 38. C2×D4×C163 | C2×C4 | semidirect |
| 41. C42×C163 | C2×C4 | semidirect |
| 91. C163 | #2127 | semidirect |
| 97. #353 | D163 | semidirect |
| 120. C2×D4 | C4×D163 | semidirect |
| 133. C42 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782228 | 2 |
| #99×D163 | 2 |
| #23781459 | 2 |
| #23781458 | 2 |
| #353×C163 | 2 |
| #2127 | 163 |