Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19104669 | C2 | semidirect |
| 2. C2×#19104667 | C2 | semidirect |
| 6. #23781531 | C2 | semidirect |
| 7. #336×C163 | C2 | semidirect |
| 99. C163 | #2092 | semidirect |
| 107. #336 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104669 | 2 |
| C2×#19104667 | 2 |
| C2×#19104657 | 2 |
| #23781567 | 2 |
| #23781531 | 2 |
| #336×C163 | 2 |
| #2092 | 163 |