Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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. C22×#14579698 | C2 | semidirect |
| 2. #23782213 | C2 | direct (N × H) |
| 3. C2×#19104735 | C2 | semidirect |
| 4. C2×#19104722 | C2 | semidirect |
| 5. C2×#19104706 | C2 | semidirect |
| 6. C2×D4×Dic163 | C2 | semidirect |
| 7. C2×C42×D163 | C2 | semidirect |
| 8. C2×#127×C163 | C2 | semidirect |
| 10. C2×#14579698 | C22 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 17. #19104722 | C22 | semidirect |
| 18. #19104706 | C22 | semidirect |
| 19. D4×Dic163 | C22 | semidirect |
| 24. C42×D163 | C22 | semidirect |
| 27. #127×C163 | C22 | semidirect |
| 41. C2×C4×D163 | D4 | semidirect |
| 69. C4×D163 | C2×D4 | semidirect |
| 77. C2×C4×C163 | #41 | semidirect |
| 90. C4×C163 | C2×#41 | semidirect |
| 95. C2×C163 | #532 | semidirect |
| 99. C163 | C2×#532 | semidirect |
| 104. C2×#127 | D163 | semidirect |
| 119. #127 | C2×D163 | semidirect |
| 177. C2×C4 | #14579698 | semidirect |
| 193. C4 | C2×#14579698 | semidirect |
| 196. C2 | #23782213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| #23782213 | 2 |
| C2×#19104735 | 2 |
| C2×#19104722 | 2 |
| C2×#19104706 | 2 |
| C2×D4×Dic163 | 2 |
| C2×C42×D163 | 2 |
| C2×#127×C163 | 2 |
| C2×#532 | 163 |