Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#14579688 | C2 | semidirect |
| 2. C2×#19104714 | C2 | semidirect |
| 4. #23781911 | C2 | direct (N × H) |
| 5. C2×#19104669 | C2 | semidirect |
| 6. C2×#19104660 | C2 | semidirect |
| 7. C2×#19104657 | C2 | semidirect |
| 8. C22×M16×C163 | C2 | semidirect |
| 13. C2×#14579688 | C22 | semidirect |
| 15. #19104714 | C22 | semidirect |
| 23. #19104669 | C22 | semidirect |
| 24. #19104660 | C22 | semidirect |
| 25. #19104657 | C22 | semidirect |
| 28. C2×M16×C163 | C22 | semidirect |
| 62. C2×C8×C163 | D4 | semidirect |
| 97. C8×C163 | C2×D4 | semidirect |
| 118. C2×C163 | #468 | semidirect |
| 123. C163 | C2×#468 | semidirect |
| 126. C22×M16 | D163 | semidirect |
| 140. C2×M16 | C2×D163 | semidirect |
| 179. C2×C8 | C22⋊D163 | semidirect |
| 221. C8 | C2×C22⋊D163 | semidirect |
| 243. C2 | #23781911 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| C2×#19104714 | 2 |
| C2×#19104709 | 2 |
| #23781911 | 2 |
| C2×#19104669 | 2 |
| C2×#19104660 | 2 |
| C2×#19104657 | 2 |
| C22×M16×C163 | 2 |
| C2×#468 | 163 |