Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×Dic326 | C2 | semidirect |
| 2. #23781998 | C2 | semidirect |
| 4. #23781969 | C2 | semidirect |
| 5. #23781884 | C2 | semidirect |
| 6. #23781820 | C2 | semidirect |
| 8. #23781770 | C2 | semidirect |
| 9. #23781765 | C2 | semidirect |
| 10. #23781722 | C2 | semidirect |
| 131. C163 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic326 | 2 |
| #23781998 | 2 |
| #23781981 | 2 |
| #23781969 | 2 |
| #23781884 | 2 |
| #23781820 | 2 |
| #23781803 | 2 |
| #23781770 | 2 |
| #23781765 | 2 |
| #23781722 | 2 |
| #529×C163 | 2 |
| #3117 | 163 |