Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19104758 | C2 | semidirect |
| 2. C2×#19104756 | C2 | semidirect |
| 3. #23782216 | C2 | semidirect |
| 4. #23782214 | C2 | semidirect |
| 5. #23782058 | C2 | semidirect |
| 6. #23782057 | C2 | semidirect |
| 7. #23782055 | C2 | semidirect |
| 8. #23782054 | C2 | semidirect |
| 9. #23782051 | C2 | semidirect |
| 10. #97×D163 | C2 | semidirect |
| 11. #497×C163 | C2 | semidirect |
| 65. C8×D163 | D4 | semidirect |
| 133. C163 | #3150 | semidirect |
| 141. #497 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×#19104756 | 2 |
| #23782216 | 2 |
| #23782214 | 2 |
| #23782058 | 2 |
| #23782057 | 2 |
| #23782055 | 2 |
| #23782054 | 2 |
| #23782051 | 2 |
| #97×D163 | 2 |
| #497×C163 | 2 |
| #3150 | 163 |