Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C22×Dic652 | C2 | semidirect |
| 4. #23781941 | C2 | direct (N × H) |
| 5. C2×#19104653 | C2 | semidirect |
| 6. C2×#108×C163 | C2 | semidirect |
| 15. C2×Dic652 | C22 | semidirect |
| 22. #19104653 | C22 | semidirect |
| 25. #108×C163 | C22 | semidirect |
| 100. C2×C163 | #473 | semidirect |
| 103. C163 | C2×#473 | semidirect |
| 109. C2×#108 | D163 | semidirect |
| 128. #108 | C2×D163 | semidirect |
| 205. C2 | #23781941 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C22×Dic652 | 2 |
| C2×#19104741 | 2 |
| #23781941 | 2 |
| C2×#19104653 | 2 |
| C2×#108×C163 | 2 |
| C2×#473 | 163 |