Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782215 | C2 | semidirect |
| 2. #23781978 | C2 | semidirect |
| 3. #23781945 | C2 | semidirect |
| 4. #23781860 | C2 | semidirect |
| 5. #23781799 | C2 | semidirect |
| 6. C4×#14579684 | C2 | semidirect |
| 7. #23781718 | C2 | semidirect |
| 8. C2×C4×D4×C163 | C2 | semidirect |
| 11. #19104735 | C22 | semidirect |
| 12. #19104732 | C22 | semidirect |
| 17. C4×D652 | C22 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 21. #19104655 | C22 | semidirect |
| 23. C4×C163⋊C8 | C22 | semidirect |
| 81. D4×C163 | #41 | semidirect |
| 88. C2×C4×C163 | D8 | semidirect |
| 120. C163 | #3100 | semidirect |
| 123. C2×C4×D4 | D163 | semidirect |
| 199. D4 | #14579699 | semidirect |
| 208. C2×C4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| #23781978 | 2 |
| #23781945 | 2 |
| #23781860 | 2 |
| #23781799 | 2 |
| C4×#14579684 | 2 |
| #23781718 | 2 |
| C2×C4×D4×C163 | 2 |
| #3100 | 163 |