Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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. C22×#14579686 | C2 | semidirect |
| 2. C22×#14579684 | C2 | semidirect |
| 3. C2×#19104732 | C2 | semidirect |
| 4. #23782055 | C2 | direct (N × H) |
| 5. C2×#19104646 | C2 | semidirect |
| 6. C2×#124×C163 | C2 | semidirect |
| 10. C2×#14579686 | C22 | semidirect |
| 12. C2×#14579684 | C22 | semidirect |
| 15. #19104732 | C22 | semidirect |
| 16. #19104646 | C22 | semidirect |
| 20. #124×C163 | C22 | semidirect |
| 32. C2×C163⋊C8 | D4 | semidirect |
| 54. C163⋊C8 | C2×D4 | semidirect |
| 84. C2×C163 | #496 | semidirect |
| 88. C163 | C2×#496 | semidirect |
| 93. C2×#124 | D163 | semidirect |
| 108. #124 | C2×D163 | semidirect |
| 174. C2 | #23782055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579686 | 2 |
| C22×#14579684 | 2 |
| C2×#19104732 | 2 |
| #23782055 | 2 |
| C2×#19104646 | 2 |
| C2×#124×C163 | 2 |
| C2×#496 | 163 |