Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23782059 | C2 | semidirect |
| 3. #23782025 | C2 | semidirect |
| 4. #23782024 | C2 | semidirect |
| 5. #23781404 | C2 | semidirect |
| 6. #23781404 | C2 | semidirect |
| 7. #329×C163 | C2 | semidirect |
| 10. #19104735 | C22 | semidirect |
| 23. #19104646 | C22 | semidirect |
| 25. #97×C163 | C22 | semidirect |
| 26. #97×C163 | C22 | semidirect |
| 107. C163 | #1659 | semidirect |
| 115. #329 | D163 | semidirect |
| 133. #97 | C2×D163 | semidirect |
| 134. #97 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782407 | 2 |
| #23782059 | 2 |
| #23782025 | 2 |
| #23782024 | 2 |
| #23781404 | 2 |
| #329×C163 | 2 |
| #1659 | 163 |