Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#19104727 | C2 | semidirect |
| 2. #23781965 | C2 | direct (N × H) |
| 3. C2×#19104668 | C2 | semidirect |
| 4. C2×#19104666 | C2 | semidirect |
| 5. C2×C4⋊(C163⋊C8) | C2 | semidirect |
| 12. #19104727 | C22 | semidirect |
| 17. #19104668 | C22 | semidirect |
| 18. #19104666 | C22 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 99. C2×C163 | #478 | semidirect |
| 103. C163 | C2×#478 | semidirect |
| 203. C2 | #23781965 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104727 | 2 |
| #23781965 | 2 |
| C2×#19104668 | 2 |
| C2×#19104666 | 2 |
| C2×C4⋊(C163⋊C8) | 2 |
| C2×#19104656 | 2 |
| C2×C4×D4×C163 | 2 |
| C2×#478 | 163 |