Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #23782139 | C2 | semidirect |
| 3. #23781778 | C2 | semidirect |
| 4. C4×D1304 | C2 | semidirect |
| 5. #23781703 | C2 | semidirect |
| 6. #23781671 | C2 | semidirect |
| 7. #405×C163 | C2 | semidirect |
| 9. C2×D1304 | C4 | semidirect |
| 12. C4×D652 | C22 | semidirect |
| 16. #19104669 | C22 | semidirect |
| 17. #19104667 | C22 | semidirect |
| 18. #19104657 | C22 | semidirect |
| 22. #97×C163 | C22 | semidirect |
| 23. C4×C8×C163 | C22 | semidirect |
| 27. C2×D652 | C2×C4 | semidirect |
| 30. D1304 | C2×C4 | semidirect |
| 31. D1304 | C2×C4 | semidirect |
| 38. C2×C8×C163 | C2×C4 | semidirect |
| 77. C163 | #2948 | semidirect |
| 85. #405 | D163 | semidirect |
| 100. #97 | C2×D163 | semidirect |
| 101. C4×C8 | C2×D163 | semidirect |
| 112. C2×C8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1304 | 2 |
| #23782139 | 2 |
| #23781778 | 2 |
| C4×D1304 | 2 |
| #23781703 | 2 |
| #23781671 | 2 |
| #405×C163 | 2 |
| #2948 | 163 |