Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4⋊Dic163 | C2 | semidirect |
| 3. #23781667 | C2 | direct (N × H) |
| 4. C2×#19104660 | C2 | semidirect |
| 5. C2×#19104657 | C2 | semidirect |
| 6. C22×M16×C163 | C2 | semidirect |
| 9. C2×#14579699 | C4 | semidirect |
| 19. C2×C4⋊Dic163 | C22 | semidirect |
| 20. #19104660 | C22 | semidirect |
| 21. #19104657 | C22 | semidirect |
| 24. C2×M16×C163 | C22 | semidirect |
| 29. #14579699 | C2×C4 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 36. C2×D652 | C2×C4 | semidirect |
| 65. Dic326 | C22×C4 | semidirect |
| 68. D652 | C22×C4 | semidirect |
| 110. C2×C163 | #417 | semidirect |
| 115. C163 | C2×#417 | semidirect |
| 118. C22×M16 | D163 | semidirect |
| 134. C2×M16 | C2×D163 | semidirect |
| 227. C2 | #23781667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C22×C4⋊Dic163 | 2 |
| #23781667 | 2 |
| C2×#19104660 | 2 |
| C2×#19104657 | 2 |
| C22×M16×C163 | 2 |
| C2×#417 | 163 |