Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19104723 | C2 | semidirect |
| 3. C2×#19104714 | C2 | semidirect |
| 4. #23781583 | C2 | semidirect |
| 5. #23781567 | C2 | semidirect |
| 6. #23781520 | C2 | semidirect |
| 7. C4×C22⋊C4×C163 | C2 | semidirect |
| 9. C22×Dic326 | C22 | semidirect |
| 16. C2×C4⋊Dic163 | C22 | semidirect |
| 17. C2×Dic163⋊C4 | C22 | semidirect |
| 19. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 23. C2×C42×C163 | C22 | semidirect |
| 24. #95×C163 | C22 | semidirect |
| 85. C22×C163 | #124 | semidirect |
| 107. C163 | #2435 | semidirect |
| 115. C4×C22⋊C4 | D163 | semidirect |
| 131. C2×C42 | C2×D163 | semidirect |
| 132. #95 | C2×D163 | semidirect |
| 199. C22 | #19104723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D652 | 2 |
| C2×#19104723 | 2 |
| C2×#19104714 | 2 |
| #23781583 | 2 |
| #23781567 | 2 |
| #23781520 | 2 |
| C4×C22⋊C4×C163 | 2 |
| #2435 | 163 |