Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 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×#14579688 | C2 | semidirect |
| 3. C2×C4×Dic326 | C2 | semidirect |
| 4. #23781866 | C2 | direct (N × H) |
| 5. C2×#19104657 | C2 | semidirect |
| 6. C2×C4⋊C8×C163 | C2 | semidirect |
| 12. C2×#14579688 | C22 | semidirect |
| 16. C4×Dic326 | C22 | semidirect |
| 20. #19104657 | C22 | semidirect |
| 23. C4⋊C8×C163 | C22 | semidirect |
| 27. C2×Dic326 | D4 | semidirect |
| 57. Dic326 | C2×D4 | semidirect |
| 69. C2×C4×C163 | SD16 | semidirect |
| 87. C4×C163 | C2×SD16 | semidirect |
| 92. C2×C163 | #460 | semidirect |
| 97. C163 | C2×#460 | semidirect |
| 103. C2×C4⋊C8 | D163 | semidirect |
| 120. C4⋊C8 | C2×D163 | semidirect |
| 167. C2×C4 | #14579688 | semidirect |
| 187. C4 | C2×#14579688 | semidirect |
| 191. C2 | #23781866 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| C2×#19104732 | 2 |
| C2×C4×Dic326 | 2 |
| #23781866 | 2 |
| C2×#19104657 | 2 |
| C2×C4⋊C8×C163 | 2 |
| C2×#460 | 163 |