Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #23781706 | C2 | semidirect |
| 4. #23781704 | C2 | semidirect |
| 5. #23781703 | C2 | semidirect |
| 6. #23781701 | C2 | semidirect |
| 7. #427×C163 | C2 | semidirect |
| 9. C2×#14579682 | C4 | semidirect |
| 20. #19104669 | C22 | semidirect |
| 21. #19104668 | C22 | semidirect |
| 22. #19104667 | C22 | semidirect |
| 23. #19104666 | C22 | semidirect |
| 26. #107×C163 | C22 | semidirect |
| 27. #106×C163 | C22 | semidirect |
| 35. #14579682 | C2×C4 | semidirect |
| 36. #14579682 | C2×C4 | semidirect |
| 37. C2×C163⋊C8 | C2×C4 | semidirect |
| 46. C2×C8×C163 | C2×C4 | semidirect |
| 87. C163 | #2911 | semidirect |
| 95. #427 | D163 | semidirect |
| 112. #107 | C2×D163 | semidirect |
| 115. #106 | C2×D163 | semidirect |
| 128. 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×#14579682 | 2 |
| #117×D163 | 2 |
| #23781706 | 2 |
| #23781704 | 2 |
| #23781703 | 2 |
| #23781701 | 2 |
| #427×C163 | 2 |
| #2911 | 163 |