Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19104663 | C2 | semidirect |
| 3. #23781664 | C2 | semidirect |
| 4. C2×#19104652 | C2 | semidirect |
| 5. #390×C163 | C2 | semidirect |
| 8. #19104780 | C4 | semidirect |
| 13. C2×#14579683 | C22 | semidirect |
| 19. C2×C4⋊C4×C163 | C22 | semidirect |
| 21. C2×C42×C163 | C22 | semidirect |
| 58. Dic326 | C22⋊C4 | semidirect |
| 60. D652 | C22⋊C4 | semidirect |
| 112. C163 | #1792 | semidirect |
| 118. #390 | D163 | semidirect |
| 128. C2×C4⋊C4 | C2×D163 | semidirect |
| 130. C2×C42 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| C2×#19104663 | 2 |
| #23781664 | 2 |
| C2×#19104652 | 2 |
| #390×C163 | 2 |
| #1792 | 163 |