Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #23782432 | C2 | semidirect |
| 3. #23781683 | C2 | semidirect |
| 4. C2×#19104663 | C2 | semidirect |
| 5. C4×#41×C163 | C2 | semidirect |
| 7. #19104782 | C4 | semidirect |
| 8. #19104781 | C4 | semidirect |
| 13. C2×#14579683 | C22 | semidirect |
| 14. #19104663 | C22 | semidirect |
| 15. #19104663 | C22 | semidirect |
| 19. #117×C163 | C22 | semidirect |
| 20. C2×C42×C163 | C22 | semidirect |
| 24. #14579699 | C2×C4 | semidirect |
| 27. C2×Dic326 | C2×C4 | semidirect |
| 29. C2×D652 | C2×C4 | semidirect |
| 83. C163 | #2901 | semidirect |
| 87. C4×#41 | D163 | semidirect |
| 101. #117 | C2×D163 | semidirect |
| 102. C2×C42 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| #23782432 | 2 |
| #23781683 | 2 |
| C2×#19104663 | 2 |
| C4×#41×C163 | 2 |
| #2901 | 163 |