Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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×#19104691 | C2 | semidirect |
| 3. #23781528 | C2 | semidirect |
| 4. #23781524 | C2 | semidirect |
| 6. #23781512 | C2 | semidirect |
| 7. #381×C163 | C2 | semidirect |
| 11. C22×C4×D163 | C4 | semidirect |
| 15. C2×Dic163⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic163 | C22 | semidirect |
| 19. C163⋊#95 | C22 | semidirect |
| 22. #95×C163 | C22 | semidirect |
| 56. C2×Dic163 | C22⋊C4 | semidirect |
| 82. C2×D163 | #117 | semidirect |
| 93. C163 | #2280 | semidirect |
| 98. #381 | D163 | semidirect |
| 116. #95 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D163 | 2 |
| C2×#19104691 | 2 |
| #23781528 | 2 |
| #23781524 | 2 |
| #23781520 | 2 |
| #23781512 | 2 |
| #381×C163 | 2 |
| #2280 | 163 |