Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781778 | C2 | semidirect |
| 3. #23781489 | C2 | semidirect |
| 4. #23781477 | C2 | semidirect |
| 5. #23781475 | C2 | semidirect |
| 6. #23781443 | C2 | semidirect |
| 7. #444×C163 | C2 | semidirect |
| 10. #19104678 | C4 | semidirect |
| 11. #19104676 | C4 | semidirect |
| 28. C163⋊C16 | C2×C4 | semidirect |
| 30. Q16×C163 | C2×C4 | semidirect |
| 32. D8×C163 | C2×C4 | semidirect |
| 68. C163 | AGL(1,ℤ/16) | semidirect |
| 71. #444 | D163 | semidirect |
| 93. Q16 | C4×D163 | semidirect |
| 97. D8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782100 | 2 |
| #23781778 | 2 |
| #23781489 | 2 |
| #23781477 | 2 |
| #23781475 | 2 |
| #23781443 | 2 |
| #444×C163 | 2 |
| AGL(1,ℤ/16) | 163 |