Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19104761 | C2 | semidirect |
| 2. C4×#14579699 | C2 | semidirect |
| 3. #23781862 | C2 | semidirect |
| 4. #23781857 | C2 | semidirect |
| 5. #23781689 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. C2×#127×C163 | C2 | semidirect |
| 10. C2×#14579687 | C22 | semidirect |
| 11. C2×#14579684 | C22 | semidirect |
| 13. C4×Dic326 | C22 | semidirect |
| 14. C4×D652 | C22 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 20. #19104656 | C22 | semidirect |
| 28. #14579699 | D4 | semidirect |
| 59. Dic326 | C2×D4 | semidirect |
| 61. D652 | C2×D4 | semidirect |
| 94. C4×C163 | AGL(1,ℤ/8) | semidirect |
| 104. C163 | #3038 | semidirect |
| 107. C2×#127 | D163 | semidirect |
| 201. C4 | #19104761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C4×#14579699 | 2 |
| #23781862 | 2 |
| #23781857 | 2 |
| #23781689 | 2 |
| #23781670 | 2 |
| C2×#127×C163 | 2 |
| #3038 | 163 |