Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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. C22⋊C8×D163 | C2 | semidirect |
| 3. #23781524 | C2 | semidirect |
| 4. #23781400 | C2 | semidirect |
| 5. #23781399 | C2 | semidirect |
| 6. #23781398 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 9. C2×D4×D163 | C4 | semidirect |
| 12. #19104710 | C4 | semidirect |
| 16. #19104706 | C4 | semidirect |
| 18. C4⋊C4×D163 | C4 | semidirect |
| 21. C22⋊(C163⋊C8) | C22 | semidirect |
| 23. C163⋊#95 | C22 | semidirect |
| 25. C22⋊C8×C163 | C22 | semidirect |
| 26. #95×C163 | C22 | semidirect |
| 140. C163 | #1519 | semidirect |
| 148. #327 | D163 | semidirect |
| 165. C22⋊C8 | C2×D163 | semidirect |
| 167. #95 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D163 | 2 |
| C22⋊C8×D163 | 2 |
| #23781524 | 2 |
| #23781400 | 2 |
| #23781399 | 2 |
| #23781398 | 2 |
| #327×C163 | 2 |
| #1519 | 163 |