Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 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. #23781786 | C2 | semidirect |
| 3. #23781777 | C2 | semidirect |
| 4. #23781489 | C2 | semidirect |
| 5. #23781476 | C2 | semidirect |
| 6. #23781442 | C2 | semidirect |
| 7. #361×C163 | C2 | semidirect |
| 11. #19104679 | C4 | semidirect |
| 12. #19104676 | C4 | semidirect |
| 23. Dic652 | C2×C4 | semidirect |
| 25. D1304 | C2×C4 | semidirect |
| 32. C163⋊C16 | C2×C4 | semidirect |
| 68. C163 | AGL(1,ℤ/16) | semidirect |
| 74. #361 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782101 | 2 |
| #23781786 | 2 |
| #23781777 | 2 |
| #23781489 | 2 |
| #23781476 | 2 |
| #23781442 | 2 |
| #361×C163 | 2 |
| AGL(1,ℤ/16) | 163 |