Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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. #23782106 | C2 | semidirect |
| 3. #23781920 | C2 | semidirect |
| 4. #23781476 | C2 | semidirect |
| 5. #23781475 | C2 | semidirect |
| 6. #23781446 | C2 | semidirect |
| 7. #510×C163 | C2 | semidirect |
| 19. #19104675 | C22 | semidirect |
| 20. #19104667 | C22 | semidirect |
| 23. C2×Q16×C163 | C22 | semidirect |
| 26. M32×C163 | C22 | semidirect |
| 106. C163 | #2191 | semidirect |
| 110. #510 | D163 | semidirect |
| 123. C2×Q16 | C2×D163 | semidirect |
| 131. M32 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782462 | 2 |
| #23782106 | 2 |
| #23781920 | 2 |
| #23781476 | 2 |
| #23781475 | 2 |
| #23781446 | 2 |
| #510×C163 | 2 |
| #2191 | 163 |