Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782470 | C2 | semidirect |
| 2. #23782101 | C2 | semidirect |
| 3. C2×#19104676 | C2 | semidirect |
| 4. #23781477 | C2 | semidirect |
| 5. #23781471 | C2 | semidirect |
| 6. #23781449 | C2 | semidirect |
| 7. #472×C163 | C2 | semidirect |
| 18. #19104675 | C22 | semidirect |
| 19. C2×C163⋊C16 | C22 | semidirect |
| 21. C2×D8×C163 | C22 | semidirect |
| 23. #108×C163 | C22 | semidirect |
| 93. C163 | #2192 | semidirect |
| 98. #472 | D163 | semidirect |
| 110. C2×D8 | C2×D163 | semidirect |
| 117. #108 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782470 | 2 |
| #23782101 | 2 |
| C2×#19104676 | 2 |
| #23781477 | 2 |
| #23781471 | 2 |
| #23781449 | 2 |
| #472×C163 | 2 |
| #2192 | 163 |