Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#14579684 | C2 | semidirect |
| 2. C2×C4×D652 | C2 | semidirect |
| 3. #23781857 | C2 | direct (N × H) |
| 4. C2×C4⋊(C163⋊C8) | C2 | semidirect |
| 5. C2×#19104656 | C2 | semidirect |
| 6. C2×#127×C163 | C2 | semidirect |
| 10. C2×#14579684 | C22 | semidirect |
| 13. C4×D652 | C22 | semidirect |
| 16. C4⋊(C163⋊C8) | C22 | semidirect |
| 17. #19104656 | C22 | semidirect |
| 22. #127×C163 | C22 | semidirect |
| 27. C2×D652 | D4 | semidirect |
| 58. D652 | C2×D4 | semidirect |
| 74. C2×C4×C163 | D8 | semidirect |
| 95. C4×C163 | C2×D8 | semidirect |
| 100. C2×C163 | #459 | semidirect |
| 105. C163 | C2×#459 | semidirect |
| 108. C2×#127 | D163 | semidirect |
| 122. #127 | C2×D163 | semidirect |
| 179. C2×C4 | #14579684 | semidirect |
| 202. C4 | C2×#14579684 | semidirect |
| 207. C2 | #23781857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| C2×C4×D652 | 2 |
| #23781857 | 2 |
| C2×C4⋊(C163⋊C8) | 2 |
| C2×#19104656 | 2 |
| C2×#127×C163 | 2 |
| C2×#459 | 163 |