Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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. #23781983 | C2 | semidirect |
| 3. #23781600 | C2 | semidirect |
| 4. #23781400 | C2 | semidirect |
| 5. #23781399 | C2 | semidirect |
| 6. #23781388 | C2 | semidirect |
| 7. #481×C163 | C2 | semidirect |
| 20. C22⋊(C163⋊C8) | C22 | semidirect |
| 21. C163⋊#95 | C22 | semidirect |
| 23. C2×C4⋊C4×C163 | C22 | semidirect |
| 26. C22⋊C8×C163 | C22 | semidirect |
| 126. C163 | #1613 | semidirect |
| 130. #481 | D163 | semidirect |
| 144. C2×C4⋊C4 | C2×D163 | semidirect |
| 152. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782223 | 2 |
| #23781983 | 2 |
| #23781600 | 2 |
| #23781400 | 2 |
| #23781399 | 2 |
| #23781388 | 2 |
| #481×C163 | 2 |
| #1613 | 163 |