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×D1304 | C2 | semidirect |
| 2. C2×#19104732 | C2 | semidirect |
| 3. C2×C4×D652 | C2 | semidirect |
| 4. #23781861 | C2 | direct (N × H) |
| 5. C2×#19104657 | C2 | semidirect |
| 6. C2×C4⋊C8×C163 | C2 | semidirect |
| 13. C2×D1304 | C22 | semidirect |
| 15. #19104732 | C22 | semidirect |
| 17. C4×D652 | C22 | semidirect |
| 20. #19104657 | C22 | semidirect |
| 23. C4⋊C8×C163 | C22 | semidirect |
| 35. C2×D652 | D4 | semidirect |
| 67. D652 | C2×D4 | semidirect |
| 73. C2×C4×C163 | D8 | semidirect |
| 95. C4×C163 | C2×D8 | semidirect |
| 99. C2×C163 | #459 | semidirect |
| 105. C163 | C2×#459 | semidirect |
| 111. C2×C4⋊C8 | D163 | semidirect |
| 128. C4⋊C8 | C2×D163 | semidirect |
| 179. C2×C4 | D1304 | semidirect |
| 202. C4 | C2×D1304 | semidirect |
| 207. C2 | #23781861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1304 | 2 |
| C2×#19104732 | 2 |
| C2×C4×D652 | 2 |
| #23781861 | 2 |
| C2×#19104657 | 2 |
| C2×C4⋊C8×C163 | 2 |
| C2×#459 | 163 |