Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
194 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 9. C4⋊Dic317 | C4 | semidirect |
| 11. C4×Dic317 | C4 | semidirect |
| 14. C4⋊C4×C317 | C4 | semidirect |
| 39. C4×C317 | C42 | semidirect |
| 42. Dic317 | C4⋊C4 | direct (N × H) |
| 50. C317 | C4×C4⋊C4 | semidirect |
| 63. C4⋊C4 | Dic317 | direct (N × H) |
| 93. C4 | C4×Dic317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic317 | 2 |
| C2×C4×Dic317 | 2 |
| #23778687 | 2 |
| C2×C4⋊C4×C317 | 2 |
| C4×C4⋊C4 | 317 |